That range will include: a) Very wet and muddy trails below the snow line; b) Then either soft snow spring snow that requires snowshoes; or c) A "spine" of snow left over from the winter's snowshoe tracks; or d) Hard ice if the temperature is still near freezing.
Given these conditions on the higher summits, lower peaks like Rooster Comb in Keene Valley or Bald Peak in New Russia are recommended until the snow melts and the trails dry out.