Help with Domino please

Im feeling sorry for Domino as he doesnt seem to cope with this wet weather very well. He's constantly wet underneath and muddy. He has deformed front feet and sits alot lower to the ground than a rabbit normally would. He and Cookie have a playhouse with a permanent run attached (on paving) and they come out twice a day for free play in the garden. This is his first winter outside since Ive had him, so its a bit of a learning curve, but Im worried about him being constantly wet all the time and the possibly impact on his health.

I have had him in and bathed and dried him, but he gets stressed being handled and I dont think this would really be an option on a daily basis.

I dont know whether to restrict him to his run and not let him out in the garden, although I feel bad about doing this as they both enjoy their free time in the garden. Or move him indoors, which will be a task in itself trying to find the space for them as I have a small house and again they will have to be restricted to a small-ish area because theres no-one to supervise them during the day and Cookie is very destructive when indoors. I feel either way their loosing out, especially Cookie because she's so lively.

Any thoughts or suggestions please. Thanks

when you say he's wet, is it cause by not eating hay w/ soft poos?

no I mean wet from being in the garden. Everywhere is boggy and sodden and whereas the other rabbits may just get wet feet, he gets completely wet and muddy all underneath, his feet, his tummy etc. He doesnt seem to dry, so remains damp all the time

Prsonally I'd keep him in the playhouse on wet days. It's not a good idea for him to be wet all the time because he could end up with sore hocks and dermatitis...buns get a condition similar to mud fever in horses if they are wet all the time