I read somewhere that it takes longer for a horse to get out of shape than we would think, since humans lose physical fitness faster than horses.  I can't figure out where I read that, though.  Any thoughts on this?

Depends on the horse and what level of fitness they were at to start with I think. And how they're kept, pastured or stalled. How old they are, etc.  If I don't ride mine for a week I can tell in their breathing. It takes a few days to get them back to normal. But their stamina & muscle strength seems to stay the same. It does take them longer than it takes me to get soft though for sure. I usually give mine December-March off and by January he's usually pretty soft. He doesn't run or move much outside though, he sleeps most of the day. My 5 year old runs enough on her own to stay in decent shape 

I good friend of mine is an indurance vet and I was able to listen to a presentation about this. He never gave a time frame, that I recall... but he did say it takes horses substantially longer than humans to lose their fitness.

Muscles in humans only take 72hrs of unuse to begin to atrophy (die). Of course horses are constantly moving but not all muscles utilized to turn barrels are used running around the pasture....on the other hand I'm not sure how long it takes equine muscles to begin to atrophy...probably around 5-7 days depending on how much they're eating.

I stand corrected. This site says 2-3 wks:

https://ker.com/equinews/muscle-atrophy-horses/

Kentucky Equine Research