I did a circumnavigation of the 48 states in 2004 - counterclockwise from my home in Florida. I did it in five stages. I get frequent flier miles from my brother so I did it in five one-month stages - storing my bike and flying home for two weeks between stages. Florida to New Hampshire; NH to Casper, Wyoming; WY to Florence, Oregon and San Francisco, CA; CA to San Antonio, TX; TX to home.
For various reasons I started too late and hit some cold weather on the last two stages but nothing I couldn't handle. I finished up in December. I didn't follow any planned route - just winged it. I recommend the ferry across Lake Michigan, US14 from Wisconsin to Yellowstone, US 26 and 126 across Idaho and Oregon and the coast route in Oregon and California. I cut inland at Guadalupe, CA because of the increasing number of pesky homeless bums in the campgrounds as I headed south. Also make sure you go along the Galveston waterfront as I did instead of going through Houston. Louisiana is a tough bicycling state. You might want to rigorously follow the ACA route there. The Gulf Coast is generally delightful but congested around the towns and cities. US 90 is an alternative but not nearly as pleasant and scenic.
2004 was a rainy year. It was the main reason I went to Ortlieb panniers and handlebar pack.