Suggest you plan to make a hardcore (or concrete if you like) area away from the gates and feed hay on it, ideally in a ring feeder (sheep size or tombstone style ideally). There will still be some pent up energy to use, especially if they're only out for an hour 4x weekly, I'd go for more personally as the work in spring won't be significantly different. But they'll have something to focus on and healthy normal activity at that. Otherwise they'll hooley and then stand at the gate bored because a trashed field has nothing in between for them.
I would use a builders bag to drag loose hay in to fill the feeder before turning out, it slides over mud and isn't heavy like a bale, but you could get a local farmer to deliver a whole bale direct to the feeder and cover it when they're not out. Think about tractor access for full bales tho, maybe over a fence with a telehandler from the yard or a good hard track rather than through your muddy gateway..
The other alternative is to loose house the horses in a barn rather than individual stables - cattle court style but less head per pen obviously. Roll out a bale of straw and deep litter it with new over the top, then get a neighbouring farmer to dig out in spring and stack a muckheap for you. Rate here is about £25/hour for tractor work.
If you're not riding daily on roads I would also recommend removing shoes over winter and letting their feet harden off. Less damage to root systems in the field means a quicker recovery and a mix of hardcore at the gate and at feeding area will improve the rest of the paddock's ability to recover quickly in spring.
I sometimes get a stubble field to graze/feed hay on over part or all of a winter which rests my grazing completely and is worth paying for. Farmer tells me which is for spring sowing, I put them on, he supplies hay direct to his own field which saves him time/makes him money and suits us both until he needs to plough in Feb. I pay the rate for sheep winter grazing.