Kaitlinb,
In September and October the Northern Tier route is likely to be perfect to cold, not likley to get much snow, and the roads are likely to be open. November is a toss up, December is cold and snowy in the Dakotas, Montana, Idaho and Washinton. The off chance of bad weather is always there but September should be no problem. A few questions I'd ask myself. How far do I plan on riding each day? When will I get over the highest passes in Washington, Idaho, and Montana? Do cold nights and cold days bother you? If you take three months to complete the trip you'll be into December in Western Montana or Idaho and that is not good. Very likely to get loads of snow there. But if you travel 100 miles per day you'll end before November and you won't likely see too much snow or super cold weather except a few high passes.
Take this for what it is worth. I started a trip in Alaska in the last few days of September in 1992. Coldest September Alaska had ever seen. It was 30 below our first night out in Fairbanks. We rode down the Alcan to Haines in snow and very cold temps, then took a ferry to Prince Rupert. It got cold again on us in BC near Prince George, and stayed that way until we got close to Vancouver, BC, Then it was nice, with the coastal weather to San Francisco. We arrived in San Fran in mid November. Over all we had a great time.
Paul Adkins