Spiti valley - which is a better time May end or June ?



Could you please suggest me what is the best period for Spiti such that (a) we can drive down to Mud in Pin valley without getting blocked by melting glacier or slush (b) drive up to Kunzum top from Losar and come back to Losar (not planning to cross Kunzum) (c) want to see at least some snow capped vistas. Please let me know which is the best time - 3rd or 4th week of May or 1st or 2nd week of June. Your help is much appreciated .
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