Being somewhere going hypo and having no remedial sugar or having used it up, dropped etc is my worse nightmare.
And as the Americans say 'Hindsight is 20/20 vision."
I must say I always check my blood sugar level before departure for exercise and top up with a little food if it is less than 6 mmol/l PLUS drop my insulin (the one(s) that will be acting for the next 12 hours after exercise. If it is 14 mmol/l or greater I delay exercise and give a correction dose, and if there is time, wait for my BSL to get done to less than 12 but > 6 mmol/l before some short, curtailed ( the exercise not the dog !) exercise. I check BSL before driving home ( and ensure it is 5 mmol/l or >) before heading off. Low doby temperature is a sign of hypo I believe, Not a cheery thought in cold weather !!
I go through a check and always carry a backpack. Glucose tabs, muesli bars, some water, spare pump supplies, insulin and pump battery or charger, money etc.
It becomes a habit, but despite the best-made plans of women, men and mice, things can still go wrong.
Maybe the dog needs to have a glucose container on his/her collar as a back -up ?