Greetings! I left Portland, OR on April 20th this spring for my solo, cross-country trip. Took the Pacific Coast route south to SF, then the Western Express east to the TransAm. I anticipated facing poor weather along the way due to the early departure. I had plenty of cold, persistent rain crossing the coastal range in Oregon and then got hammered by a nasty storm in northern California (wind, cold, rain, etc) for 2 days. When I got to SF ~1 wk out from Portland, Carson Pass was getting a fresh layer of snow. I ended up waiting in SF for a couple days while that storm passed. There was still tons of snow on the ground when I crossed - Sections had walls of snow rising right from the shoulder. Slightly concerning! Makes you push it a little more. Up to that point, I don't think the night-time lows dropped under the upper 30s.
Nevada consisted of high winds, but mostly sun. Utah was a beast from a weather standpoint after a beautiful couple of days in Zion. My night in Bryce Canyon consisted of lows in the 30s and some sleet. I left a day early, b/c they were expecting snow and lows in the 20s. Outside Escalante, I encountered some ridiculous, ride-in-the-middle-of-the-road-so-you're-not-blown-off winds just before the snow came. Snowed the entire way up Boulder Mtn. I got lucky in Colorado, as I only had some intermittent rain. Apparently Monarch Pass was a complete nightmare a couple days before I went through.
The real pain for me began once I got out of the mountains and passed Pueblo. Eastern Colorado and Kansas were just painful after cycling the Oregon and California coast, camping in the Redwoods, seeing the Sierras, going through great basin territory in Nevada, finally experiencing Abbey's country (Zion/Bryce/Glen Canyon), and cranking up and down Colorado. I could put up w/ intermittent crappy weather in such amazing parts of the country, but getting stuck in hailstorms in the middle of Kansas was not fun! And don't get me started about the dogs in Kentucky.
So yeah, leaving early may increase your chances of finding yourself in some nasty weather. In my case, I had a short time frame (only had 2 days off through Colorado) and it was likely a now-or-never chance to do the trip. So I say leave as late as you can, but definitely leave! Don't let the possibility of poor weather dissuade you. Make sure you have legitimate rain gear and some cold protection (I had my down jacket and vest through Colorado). I used the ACA maps, which were a blessing. Let me know if you have any specific questions for me. Despite some poor weather along the way, there were plenty of beautiful days and the trip overall went great. Ride on!
