Great advice so far!
As a Finnish person said, “there’s no such thing as bad weather, only bad clothes”. An I believe it! I learned to dress for the cold in cold climates when riding.
I wear cheaper fleece breeches when cold, because I can’t afford the expensive ones. I never complain about them - you don’t have to spend a lot to be warm. I have a heavier-weight knee patch fleece breech which I’ve never been cold in. They are also relatively wind-proof because the fleece is on the inside and the outer layer is smooth. When cold, I wear them or regular breeches with bona-fide wool ski socks. With knee high thick wool ski socks - my legs aren’t cold! Some wool ski socks are thin enough to ride with under dress boots. I have two pairs of paddocks made for cold weather - Ariat Frostbiters I got in Pgh and slightly lighter-weight Ariat…H2O?.. (I can’t remember but they are lined for cold weather).
Gloves. I Love Love Love Roeckl Polartec Power Stretch Pro. They are warm, stretchy and grippy enough for somewhat cold weather. When really cold, I use the bulkier (I can’t remember who makes them but they’re called) Winter Training Glove. They have less padding on rein side of the rein fingers and more on the outside to make them feel less bulky. The cheap-o approach is to wear tight fingerless “undergloves” or even you can make your own by cutting finger and a thumb hole from knee high nylons.
On my body, I wear a cheap cotton/nylon tight camisole, then a turtleneck and then a sweater over that for layers. Depending on the weather, a riding coat over that or maybe just a riding vest. When really cold, I wear silk undershirts or turtlenecks, or wool undershirts.
On my head, I will wear a fleece headband but I really really love the Kerrits fleece headband because it it THIN and fits so well under my helmet. The headbands for skiing or other things aren’t so thin and can be bulky under my helmet. That said, I wore them for years until this year I discovered the Kerrits headband.
In addition, I have a super-cheap silk scarf that I’ll use around my neck that is so freakishly warm.
I know you do not have to have a lot of money to dress warmly!
Good luck!