If you can get there you will probably get a spot-if it is opened. I don't think it is opened yet. Also, accessing Dog Valley might not be possible unless you have a snowmobile. I just checked and the National Forest site https://www.fs.usda.gov/recarea/htnf/recarea/?recid=65264 says it opens in June. My experience is that it opens in June.
Yes, but keep in mind the snow can be very deep this time of year.
Thanks! Your answer is awaiting moderation.