It really depends on the footing. My barn doesn’t have an indoor either, but we usually don’t cancel unless it is really cold (like 15*F and windy!) or if the footing is bad. If the footing is icy, really snowy, or really hard (which tends to happen when it’s this cold, it just freezes) then we can’t really ride.
If the ground is hard, wet or slippery I wouldn't ride.
Personally I think it is fine as t long as you make sure to warm up and warm down your horse.
If it’s -20 I think it’s okay if you just walk maybe trot and give your horse tons of time to cools off and make sure they don’t sweat
Hey Kaylee! I would say that for an indoor arena 20-25* is okay. For an outdoor arena I would say 25-30*. Since they are exposed to open air it could be harder on their lungs and the ground could freeze and hurt their legs. I would say walking around with a cooler is okay but no work in under 25* outside. I hope this helps! Happy new year!