What is Mt Rainier like in late June?

I'm new to the group and my honeymoon is planning around late June 2027 at Mt Rainier. Will it be too cold? I've seen some research that it'll be high of 60° and lingering snow. the whole point of going at this time of year will be to celebrate our first wedding anniversary. That time of year seemed like a good time to avoid large crowds as well. What would the weather be like?