Yes it can be a problem. I tend to keep my older short wigs for when I am doing horsey things. If riding just put riding hat on top of wig. Otherwise I usually wear some kind of hat, depending on weather. Base ball hat, wooly hat etc.
All my friends know I wear a wig, so not a shock for them if they see me in day with short hair and longer hair in evening.
How do you cope?
A couple of the girls I look after in NZ with Freedom Wigs are horse ladies. Both tend to wear their older wigs for riding and a helmet over the top.
I think Tufty has some great tips as well. Something that isn't your best hair would be a good way to deal with things.
I've spent my whole life riding and when I got my first wig, all I could think about was having to wear a helmet... ugh! But it's turned out not to be as bad as I thought. :) I usually wear a clip in topper that I put up in a ponytail (with my real hair) and wear a hat. If I'm just hacking around I'll just wear the hat, no need to do anything. If I'm jumping or taking him on a trail ride or something, I always wear a helmet... The trick is just not letting people see me. My helmet was fit when I was practically bald so a wig or something is not going to fit. So, I just keep my helmet in my car and go out to the parking lot to "grab my helmet"/sit in my car and take my wig off/put my helmet on lol. It's a bit of a hassle but I feel MUCH more comfortable wearing a helmet without hair!