The closer to the end of April you get, the less chance that snow will be an issue. Can it happen, sure, but we've had to use 4x4 to get out of a campsite with 6"+ of snow on July 4th up on the Flat Tops, so no month is totally without risk.
Yes there are alternatives. Just because we get a dump here in CO doesn't mean that I-80 through Wyoming won't be good. Just depends on the storm track. Fifty miles north or south can mean the difference between 8" and a dusting. Been happening a lot this winter.