Snow bunting plumage

My question is not an "identify this" as I know these are Snow Bunting. We have been lucky to have a small flock of 8 birds on the beach for the last few months. I think they will migrate (to Iceland?) in March. I also think the male is the paler bird. Is that right? My question is, when will the male change to it's summer plumage? Might I get to see it before it goes?