Depends. On the mountains it's VERY cold, in the city it's like 1-2 degrees in the morning. I don't mind working and dressed for work in the cold but you can't ride a horse with the stuff i wear at work.
If you're going to ride a lot in winter, and this is likely to come up, it might be a good idea to get something that'll keep you warm enough. You are warmer riding than just standing around. Long johns under jeans will probably keep your legs warm enough. I assume you ride in jeans, or do you have those skintight riding pants? I like them, and they make some that are quite warm for winter. But probably long johns are easier to get, cheaper, and maybe you have them already. On top, I layer: a T-shirt, a flannel shirt, a heavy sweater, and a winter coat. I like a short coat rather than one that comes over the hips and restricts you, unless it's a duster like you saw me wearing, which is meant for riding. Then you'll want gloves that are warm but not restricting and have a grip on the hand so the reins don't slip
through your fingers. They make fleece winter riding gloves, and I've found them for less than $10. They have some sort of leather-like plastic on the palms and fingers. Gloves made to drive a car would probably work. You'll want to cover your ears. Do you wear a riding helmet? If so, I've found that a thin fleece headband under the helmet will cover my ears, and the helmet covers my head pretty well. I have a fleece balaklava for really cold days when my cheeks feel like they'll freeze, but this is inconvenient, and I only wear it if desperate, and if it's above freezing, you won't need that much protection, though everyone's different, and some people are more sensitive to the cold than others. Why I don't like the balaklava is that if I pull it up over my mouth, my breath condenses on it and makes it wet. Very uncomfortable and yukky.
I'll ride if it's 15 degrees F or warmer, unless the wind is enough to make it a lot colder. I'll ride in light snow or light rain but not a blizzard or downpour, though sometimes I've been caught in worse weather than I had planned on.
So think about collecting the clothes for cold weather riding. Do you have
thrift shops there? Here, you can
buy used clothes very cheaply in them. A good laundering takes care of any germs you may be wary of.