Yes, a tarp/bivy/bag will work.. I've only been to the rockies August-October as I have to fly out there from the east coast so not much spring experience..

As I noted, the rockies are where I've used the bivy setup the most..

I was rained on at some point every night I've spent in a bivy on one of the RMNP trips

If I had to choose only one shelter.. I'd get a solo tent, if you want your dog inside get a lightweight two person or a biggest solo carefully seeing how much floor space you are after.

I now lean more toward bomber tents in the mountains having enjoyed storms and some snow dumps... My tarptent are used in the forests in milder months where the mesh and ventilation are welcome

I've had some enjoyable winter hiking trips, but they have only been good if the snow is good and not anywhere near melting slushy and the temps are not prolonged really really cold..

I had a 5 day stretch in the NE where most temps were below zero or in single digits.. learned a lot on that trip on dealing with cold on a mulitple day trip, but it was not fun....