Our barn has no indoor which means that riding is rarely possible when it rains. But that doesn't mean there's nothing horse-related to do - both with a horse and without one. Here are some things I've come up with - what else can you think of?
With a horse - some of these can be done in the stall and even when it isn't raining with a horse who's on stall rest:
1. Do a really thorough grooming.
2. Teach your horse to take one step back with just a hand gesture.
3. Teach your horse to take one step back and wait to accept a treat - clicker works well for this.
4. Do some basic in-hand exercises - head down, baby flexions - with a halter or bridle.
5. Teach your horse basic targeting using clicker (don't do any scary object work where the horse is in a confined space).
6. Teach your horse to accept your touch on various parts of the body - ears, belly, underside of tail, etc.
7. Teach your horse to pick up - and hold up - each foot more easily.
8. Do carrot stretches and belly lifts and tummy tucks to improve your horse's flexibility and core strength.
9. Teach your horse to move away - backwards or sideways - with a very soft touch.
10. Trim a mane, bridlepath or feathers with clippers - if your horse isn't afraid of them (otherwise work on this first as scary object training when more space is available).
Without a horse:
1. Set up a barn book, containing records for each horse of vaccinations, deworming and other health matters.
2. Give your tack a thorough cleaning, checking for wear and safety issues.
3. Organize your truck/storage area for grooming supplies and tack.
4. Wash and disinfect your brushes.
5. Make sure your medical supplies are organized and that any out-of-date items are replaced.
6. If you trailer, take your trailer in for a safety check.
7. If you trailer, make sure you have all the necessary items for trailering safely.
8. If you trailer and have a tack/dressing room, clean it out and organize it.
9. Read a book about working with horses, or watch a video - even one from an unfamiliar discipline or a clinician you aren't familiar with or maybe don't agree with.
10. Find out if there are any clinics near you that you can audit (generally much cheaper than riding) - either with a clinician you may want to ride with in the future, one you admire or even one from a completely unfamiliar discipline.
11. Order some end-of-season (and with luck on sale) barn items or horse or people clothing.
12. Organize any out-of-season horse clothing and take it in to be washed, mended and rewaterproofed (or do these things yourself).
13. Wash any dirty horse laundry - polos, saddlepads, etc.
14. Figure out if you have tack or gear that should be resold or donated and make arrangements to do so.
15. Check your horse's stall or paddock for safety issues including protruding splinters or nails.
Leave more ideas in the comments!