Note that the columns on the left show current snow water equivalent (not snow depth) as of the day you look. The column on the right is total precipitation for the year. For the Winds, you want the Wind River Basin for the east side and the Upper Green River Basin for the west side.
Total precip. was normal this past winter, but it looks as though it's melting faster than normal. Despite this, I'd expect plenty of snow left in mid- June and very high streams to ford.