This depends a lot on the type of exercising you’re doing. If you’re doing aerobic exercise, you can absolutely count on a drop in bg unless you adjust your basal rate (on a pump) or take in carbs while exercising (“feeding your basal”). Alternatively, you may be able to time your long-acting insulin shots so that you’re exercising when your long-acting insulin is at it’s lowest point. What insulin are you using?
Your basal insulin needs should generally go down while you’re doing aerobic exercise, and that can result in lows. If you make your exercise more anaerobic or you work your muscles more, you may not experience the same problems. If I’m really working my muscles, but I’m not doing any kind of aerobic exercise, then I’m actually likely to go high.
I’ve also found that exercising in the heat sends my bg levels up, but exercising in the cold does the opposite. Or for swimming, exercising in the cold keeps my bg pretty steady. Swimming in a warm pool will send me soaring though.
A lot of this is just trial and error. You’ll have to find the best way to counter lows as a result of aerobic exercise. Recognizing that, most likely, they will happen can help you be ready for them.
Exercise is really good for all other aspects of diabetes though, so please don’t let anyone’s posts discourage you from doing it! It significantly affects my insulin sensitivity which helps me a lot with post-meal spikes.