The next day, we were driving to Jasper in the same weather, only to get to the village where it was snowing like Christmas Eve. Our plan of camping was quickly thrown out the car window and we were lucky to find a room in an airbnb in the village. When we woke up the next morning, there was still snow on the ground and we still could not see the mountains as we made our way to Five Lakes trail, but at least it wasn't snowing or raining anymore. During our walk along the trail, as the wind shifted the clouds, we could see the silhouette of the enormous mountains surrounding us, but still no luck seeing the summit or getting a clear view.
It turns out that we worried all for nothing as the very next day, as we were driving through the Icefield Parkways on our way to Banff, the sun finally came out and we enjoyed two days of clear blue sky and enough mountain views to last me a few years.