Well one has to visit evey place in every season but I'm afraid this can't go for Rajasthan.
you should visit them during two seasons
Post mid monsoon and winters.
Also it depends on places for instance
Jaisalmer and bikaner : August- Sep and December till February (prefer when it's chilly in north India cos days are still warm in desert regions)
Udaipur one should visit in monsoon as it is green and post October till January (from February it starts getting drier)