Traveling Banff in December

Hello Guys, I am will travel through Banff in upcoming December. We are very excited and usually we like to do long hikes that might even be strenous. Moreover, we will start our roadtrip in Calgary, stop by in Banff first, continue to Jasper and return to Calgary with a stop in Golden.

Do you guys have insider info or suggestions what to consider or which trails are accessable without certain gear?