Canadian roofing company wanting to do roofing in a warm state for the winter
First of all, with a business such as roofing, where the work is usually handled by the owner, you would have to have a valid working permit, which usually comes with appropriate visa. Good news is currently its possible to get some sort of investor visa if you open a US company and make an investment (however, for more details on what the process is and what size of investment is needed I would recommend you to contact an immigration attorney).
It is certainly possible for a non-U.S. resident to register and maintain a U.S. company, without being required to have a U.S. address or social security number. You may even list your Canadian company as the owner, and use the same business address and name, as long as no other company has a name too similar previously registered.
You would be able to apply to form a business any state, such as Texas, Arizona or California directly online, without being required to submit any financial or identification documents. If you want your company to operate in more than one state you would need to register it in each state where you would be conducting your business (as foreign entity).