Morraine Lake road is closed for winters. If you want to go before the May opening you have to XC ski in.
There is a decent size parking lot at Lake Louise, it's going to depend on events, day, time etc if you can find a spot. If you are mid week you should be OK. Here's the LL lot:
https://maps.app.goo.gl/bUjRdKM84BsJwT2d9