Right time is medication dependent
Exercise Right recommends timing sessions so that medications can be in full effect (e.g. in PD you may experience an increase in symptoms just before the next medication dose is due). Work in conjunction with you doctor or specialist to find out about timings of medication dose and full effect.
At this time of day, levels of the hormone cortisol are higher, which lowers insulin action and keeps blood glucose levels from dropping, and circulating. Insulin is also lower (prior to any insulin taken for breakfast).
Exercise before bed is also not recommended given the risk of delayed post exercise hypoglycaemia.
When possible, scheduling similar timing of exercise into your daily routine maybe beneficial to minimize the risk of nocturnal hypoglycaemia.
A recent study published in the Journal of Diabetes Science and Technology early in 2015 found that overall, hypos occurred significantly less often following 7 AM exercise compared to 4 PM (5.6 vs. 10.7 hypos per person). That study compared blood glucose levels and the number of lows during and following moderate exercise for 36 hours.
Remember to always consult a professional before beginning any new exercise routine, and to find out what time may work best for you and your uniqueness.