Corporations don't work. Corporations do not travel across borders. People do those things. Now they may do those things on behalf of corporations, either as officers or employees or directors.
Corporations cannot receive visas, therefore. Only people can. For a person to work in the US, the person must have an appropriate immigration status, and possibly a work authorization. (Canadians don't need actual visas for most US immigration statuses; they can just show up at the border and ask to be admitted in the appropriate status.)
If you, as a Canadian, are present in the US in an immigration status that does not permit work, you are not generally allowed to do any work for your Canadian corporation. To get permission to work in the US, however, you generally need to have a job in the US with an employer willing to sponsor you, or you need to be starting a company in the US that will create jobs for US workers.
In short, if you're planning to support yourself during a period of study in the US by running a business in Canada remotely from the US, think again. On the other hand, if your business can run itself without any input from you, you can collect income from the business.