Well I lived in Northern BC my whole life, particularly in the north peace region around fort st john, and they get a ton of snow and it can get cold, they had -35C - -40C weather about a week ago. There is a horse community there but be prepared for snow and cold. Also it is very expensive to live up there right now, housing is very pricy.
The Prince George region might be nice for you, although we get a ton of snow, and it can get cold, but most of the time its a rather mild winter temp wise. But there is a lot of horse stuff always going on here, there are numerous barns and arenas around. Williams lake and the surrounding regions could be a nice fit, but again can get lots of snow, and can get lower temps.
The Okanogan has nice mild winters (most of the time). And there is lots of horse shows and events down there to. As for it being expensive to live there it can go either way. Also depends on if your wanting to rent or buy. For instance, I have a friend who lives there and she's trying to sell her apartment and she wont get hardly anything for it.
I could probably go on and on, but I haven't had my coffee yet, and my brain isn't working yet lol, but Good luck with your search.