The best time to visit Rajasthan is in autumn and winter, when the temperatures during the day are pleasant (around 25 degrees).
May and June are very hot, so better to avoid these months.
Travelling in Rajasthan during the monsoon season (July to September) is fine because it doesn't rain a lot in this part of India (Rajasthan is quite dry overall).
https://www.rajasthandriver.com/travel-info/best-time-to-visit-rajasthan-climate-weather/
November to February is an ideal time to visit Rajasthan. Neither heat will be high nor chillness will dip, but December to January is called as coldest month of Rajasthan.
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)