Can you wear gloves attached to your belt loop?

Short answer-No.
Look at the AR 670-1 under Para 3-6a. You're only authorized to wear Keys used in the performance of CQ, Armorer or duty NCO/ Officer. Or 3-6b Discusses authorized electronic devices and finally 3-6c gives the commander the authority to determine that wear is not appropriate and negate para a and b.

Stow them in your cargo pockets like we've done since time immemorial as this paragraph has changed little at least since the 80's with exception of allowing an electronic device.

According to AR 600-CommonSense, putting something on your uniform that makes it no longer uniform is a bad idea. Belt loops are for holding belts, not for hanging things off of. Would you feel the same about someone who hung a 'biner on their belt loop, and then suspended keys, a lucky rabbit's foot, and some fuzzy dice?

You have pockets. Use them. Or... just keep your gloves on your hands, where they belong!

I beg to disagree, cargo pocket, jacket pocket etc. the rule of thumb is that is the item is not covered it is not authorized. He uniform has ample pockets so that’s Soldiers can carry what they require for duty. Your unit should have guidelines and policies. Your belt loops, are just that to support a belt. Let your conscience be your guide. Thank you for your service.