We like our horses to go out every day, but appreciate this is not always possible.
If you have time to wait 5/10 mins, (and the weather is ok), it is so good for them to go out with no rug on if they have got hot when they've been ridden, just to have a good muddy roll. They need the chance to be horses especially when they are layered up with rugs 23 hours a day - imagine how itchy it must be?! Horses are meant to be muddy!
The other thing the horses love is when we turn them out for 5/10 minutes with no rugs in the snow - yes even the clipped ones! They go crazy, and roll continuously, dig and get covered. Only do this with a horse that's really easy to catch though or it could get really cold if you don't get those rugs back on fairly quick. But again, when they are heavily rugged all the time, it's such a nice freshen up for them.
Salt licks and hay in the fields - we put the 'rockie' salt licks in the fields, (the brick like ones) as they are full of vitamins and minerals but not sugar. When the grass is so scarce it does them good to just have a few extra nutrients, and keeps their mind interested. If fields are too wet (as they are currently), then one of these in the stable alongside their stable salt lick is still good.
We turn out with no hay at 8am, then hay at 12pm and the horses are brought in at 4pm. (Weather dependant). Our horses choose when they want to come in within reason, but appreciate not every horse has this luxury if their owners are at work - see if someone at the yard can bring in your horse when all the others come in, or can hay your horse at lunchtime for you, so they haven't finished all their hay by 9am and are starving until they come in...not to mention the broken fencing that comes with bored, hungry horses...
If the weather is miserable we mix alfa a into their hay.
A ball in their field for them to play with can be helpful if they have to spend a lot of their time out without much to eat.
IF TURNOUT IS NOT POSSIBLE
Try and get your horse out of the stable morning and evening for a leg stretch, as well as when it's ridden. Otherwise they just get stiff and bored. It's no good for their gut or muscles either. If the yard has no walker, there are various ways to do this. Even with a walker, I prefer to take them on a walk where they can pick at grass but time doesn't always allow.
Take them for a walk in hand, ideally where there is some good grass to pick at.
Go on a hack and ride and lead. Try to avoid rugs for the horse being led as it's shoulder's are always being rubbed otherwise. If cold, we put a roller and exercise sheet on and florescent boots, so should the horse get loose it can be seen. This way the horse being led can be schooled/ridden once and led out on a hack once; leaving it's stable twice but not overdoing the exercise.
If not that sensible/or short of time... (sensible ones can do this too!)
See if you can turn out in the school for example while you muck out. Take the rugs off as your horse won't be in there that long, but they can buck and roll and have a bit of fun, feeling refreshed when you put them back in; just flick the sand off and rug back up. Even if they don't like being left in there alone the first few times, they soon come to appreciate the freedom, and it saves them getting in the way of you mucking out!
Loose lunge (just on a headcollar or bridle with no lunging aids).
All our horses have two salt licks all year round for different minerals (and taste). They have a Himalayan salt lick, which is on a string, and a rockie salt lick on the floor (when dry this goes in the field). Make sure these licks are low in sugar and energy, it's not fair to have them bouncing off the walls with energy and it will actually make them hungrier and more irritable.
Other things you can do is put apples in their water (keeps them hydrated when eating a lot of dry hay, plus apple bobbing is a good game!)
And/or add alfa a and break up some carrots and mix with the hay to go in their haynet - hard work for them but rewarding, and more concentration is required!
The boredom breaker balls that you fill with pony nuts are great, and if you mix that with chaff it is quieter for the other horses that don't have one and it takes forever to get the nuts out. Be prepared to muck out a messy bed in the morning though!
2 haynets, either side of the stable, maybe one with hay and one with haylage can reduce boredom, but be careful if your horse is already slightly inclined towards box-walking.
A mirror in the stable can relieve boredom and can reduce/stop box walking
Feed Cool, Calm and Collected to reduce anxiety and stress.
Horses should have their rugs taken off at least once a day but ideally twice, even if this is just to take them off and put back on. If short of time, get a massage brush or curry comb (depending on how sensitive your horse is - some of our fully clipped ones love the plastic curry comb!) and massage in strong, quick circular movements around their whole body - most of them love it and will groom you back! Some will only take a really soft goat's hair brush.
For me, this is far far more important than having them clean and looking presentable - it is natural for a horse to be caked in mud, but not for them to be rugged up and they get so itchy, so if this is all you have time to do, don't worry about the mud too much, as long as it doesn't have mud fever and the mud isn't going to rub anything (e.g. if riding make sure the mud is at least brushed off where the tack is going to go.)
The other thing you can do is teach your horse 'tricks' or commands... again, mental stimulation where physical may not be possible, and also teach them carrot stretches, where they really have to reach and stretch, so they don't feel so stiff. We try and stretch them after riding (when the muscles are warm) and in the evening before leaving, whether this is when they've come in from the field or come back from their evening walk/loose school/graze (again, stretching warm muscles to avoid injury).
Personally I think this is really important... if a horse is living in, and the only chance it's ever going to have to roll is in it's stable, give it every chance to roll. I know horses are extremely expensive beings to keep, but if you can provide them with rubber matting and a deep bed so they feel comfortable rolling, they will be much happier, and try to give them a chance to roll with their rugs off at least once a day (e.g. after riding leave them loose in a skipped out stable while you put your tack away.)
Try to avoid leaving beds up to save bedding; lots of horses won't wee if the bed is up, and that can cause no end of problems, kidney infections, stuffiness when riding etc, especially if you want to ride in the afternoon and the bed went up in the morning. It will cost you more in money and stress in the long run!
If you do all these your horse will probably be exhausted going into summer, but will at least have enjoyed the winter!
Whoops...got a bit carried away! At least we love our ponies :)
Hope this is vaguely helpful :)