Pathophysiology. While exercise is helpful in everyone, it's not the main treatment for you. You are a type 1 diabetic, so you have diabetes because your body is not making enough insulin. The main treatment is to find the right Insulin regimen for you. If you wake up with bad sugars, it might be because your basal rate is too low, not because you are not exericising enough or eat the right food.
If bad means low. If you meant waking up with low bs (hypoglycemia), then it's not surprising if you underwent rigorous physical activities the day before. Doubling your bedtime carb snack can alleviate this issue but if not sufficient, I would consider lowering your night time long acting insulin. Discuss this with your endocrinologist or cde today.