I think it is two weeks too early.

I live in Wyoming and have biked to Alaska, the Yukon, and the NWT many times.
I have biked many sections and similar dirt roads in all seasons.

Yes, they start the GDMBR race in early June, but it's iffy.
Last year, I met a woman in Montana who was nearly hypothermic.

It is hard to predict how much more snow the mountains will get in April/May.
Most of the Northern Rockies have received average to average-plus snow so far.
If the heavy rains that hit California this winter retreat northward,
then there could still be a lot more snowfall.

I have skied on deep, fresh snow in early June in Wyoming many times.