Is it legal to cover your face for non-religious reasons in America?

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The laws vary from state to state. In Minnesota, it's illegal to be in public with your face covered except for religious reasons, or if you're performing some kind of amusement or entertainment, or protecting your face from the weather.

If you're just wearing a ski mask around town, and it isn't cold outside, you can expect to be arrested. Similarly, if you're running around town dressed as Batman and wearing a Batman mask, you can also expect to be arrested.

There is nothing preventing you from wearing a mask in public in the United States. That doesn't mean that the police can't stop you and see what you're up to if you're spotted on the street. It also doesn't mean that you should expect to walk into a bank or convenience store and not create a disturbance. Plan accordingly.

I assume it gets cold in Canada. I know it gets cold here in Minnesota in the winter. And I walk around with my face covered with a scarf when it gets extra cold.

And, in the US, you can also walk around with your face covered FOR religious purposes. We have "Freedom of Religion" here. I believe they have something similar in Canada, too. But I'm not too sure about France.

you can wear whatever you want here, but it's not like walking around in broad daylight with a ski mask on isn't going to draw any attention.

It may bring suspition but you can wear what ever you want, unless it's a shirt that says "i'm going to kill obama" or something that's a threat to a person or place.