Gosh I rode in a lesson today and it was 12 degrees. I was in an indoor. I actually had to shed my coat a fourth of the way thru, I had on plenty of layers plus hand warmers and toe warmers in my boots. It was really just fine and my horse did great too. My trainer was also riding, don't think he wanted to be standing around. We had everything set before hand and we pretty much both rode non stop for an hour and 15 minutes. Sometimes he rode behind me and sometimes in front of me and it was a helpful way to have him demo certain things we were working on. It was actually fun. My horse didn't break a sweat at any point (he is one of my field hunters and is very fit) and I tossed a cooler on him after wards for about 30 minutes and he was ready to re-blanket etc.
Cold has never been a big deal to me, but let it get above 85 degrees with humidity and I completely wimp out....after all you can only take but so many clothes off in the summer....
OP, I don't blame you for cancelling! I teach as well, and it's not fun when you're shivering so much it's hard to speak. I power-sweep at the end of the night just to warm myself up before I go home. Everyone kind of knows that sweeping is MY job when it's this cold!
Riding when it's super cold out doesn't bother me at all, although I don't ride very hard when it's below 15. Just w/t/c in the indoor, and usually for less than 20 minutes. My horse needs the mental stimulation.
Around here we don't think it's cold enough to consider cancelling lessons until it gets to 5F. I don't stop riding until it's -13F, and sometimes I will even go for a little w/t below that. But then these are normal temperatures for our winters, and we and the horses acclimate. We figure out how to minimize sweat and how to dry off a sweaty horse (and to a point the colder temp actually helps because the sweat blows off the horse as steam and he doesn't get wet until he's much hotter, or he slows down).
Horses are cold weather creatures - much more than we are. They can tolerate much colder air without damaging their airways because they have large sinuses to warm and moisturize the air long before it reaches their lungs. Of course cold air can damage their airways if it's cold enough or the horse is breathing hard for long enough, but they can tolerate it longer than we can. They are amazing creatures.
I think petty name-calling and that sort of rudeness is totally uncalled for. You make your own choices based on what you think is best, period.
The past three days here have been the coldest we've had this season, with temps hovering between single-digits and upper teens, and sometimes high winds. I rode today for the first time in those three days. I have asthma and cold dry air is difficult for me, so on those cold days that I am having trouble breathing I tend to err on the side of caution and ride fewer horses. I generally teach as long as students want to ride, however I keep lessons inside and I am very careful with the little ones who tend to get chilled more easily. As long as I layer up and keep moving, I don't get too cold.
I have read, as well as been told by several vets, that it takes VERY cold temps to endanger a healthy horse's respiratory function. The air passages are very long, which allows significant warming before the air reaches the lungs. I worry more about cold muscles, but as long as you keep clipped horses covered until they are warm and take care with your warm up and cool off, low positive temperatures are not necessarily dangerous. Horses are much better equipped and tolerate the cold far better than we do.
That said, I do not think you were in the wrong to cancel. Everyone has a different tolerance for the cold and there is no reason to make yourself unreasonably uncomfortable and put yourself at risk for the sake of appearing "tough". There are other factors to consider as well- horses acting up in the cold (my rides were wild today), frozen ground, water intake, etc. If you are in an area where the current temperatures are unusual, neither you nor the horses are acclimated and that can be stressful. Don't let others' rude remarks get you down! Stay warm!