I’ll start out by confessing that I haven’t rigorously exercised regularly in several years, but when I did (playing Ice Hockey) I was always best off going into the exercise with a BG of about 140 - perhaps higher if I had some insulin on-board from a recent meal. If my blood sugar is high (200+), my muscles would ache and I would become winded much faster than if my BG was lower.
I have heard that it’s not good to exercise if your BG is high. I’m not sure why, but if I try to fabricate a reason in my mind (disclaimer: this might be 100% wrong) I’d guess that it’s because you simply don’t have enough insulin in your body. Remember that insulin allows glucose to get from the bloodstream into the cells, it doesn’t just lower BG. So if you’re exercising, have lots of sugar in your blood, but run out of insulin and can’t give that energy to your muscles that need it, you become fatigued and could go into DKA. Again, could be completely wrong.
A high-protein or a high-fat (I know, that seems to contradict the whole point of exercise) meal may be a good idea for you, to try to sustain your levels during exercise. Immediately - and for several hours afterwards - take less insulin or eat more low-fat carbs to keep yourself in control.
Another side note: I’ve tried bringing my meter with me to the players bench at the hockey rink, but it was too cold and would never work. Sigh.