Menopause doesn't "stop." It means the time period after your last period.
I started riding about a year before my periods stopped (I was young). So, at first, I dealt with perimenopause symptoms and PMS affecting my riding. But, once I stopped having periods, I didn't seem to be affected. I do think your tolerance to heat can change, though. I know that I continued to have a few hot flashes for quite a few years after my periods stopped. Interestingly, it never happened when I was riding.
I generally run "hot," at least compared to my husband. I am a big head "sweater," so taking off a head cover is a big help at this in between time of year, where it may be cold when I start. Although temperatures in the 50s (F) are my ideal to ride in, they are also the hardest for me to dress for. I always seem to get warmer pretty fast, so I will wear a short sleeved jersey, maybe a sleeveless base layer, and a vest and arm warmers, so I can peel the layers off. My DH will be wearing a long sleved base layer over a long sleeved jersey and a jacket.