If you're following an evening schedule (weight training /cardio) then it's better to stick to that and meanwhile in the mornings do some basic stretches for 10-12 mins and maybe if time permits do some yoga asanas. That'll get you ready for the day ahead and keep drinking a lot of water throughout the day. But, in case you want to switch the routine then experiment a bit because Ultimately, it's you who has to understand your body and decide what's best for you.
I would rather have a short exercise in the morning. Quick active stretch and some cardio exercises to get yourself ready for the day. It would boost your energy and you would feel happier and accomplished that you did it.