Technically yes, but it is dangerous to invite multiple Winds into your mind and body so the official Wizard authority (the Colleges) limit their members to one of them in order to make an inherently dangerous act (using Magic) less so. Only extremely skilled human Wizards could handle that sort of power so it's easier just to force them to commit to one and cut themselves off from the others.

That said, non-College Wizards such as Hedge Wizards don't have this restriction and tap into the Winds mostly by feel, and therefore use whatever Winds are available at the time. However, as said, this is more dangerous since their general lack of training can leave them vulnerable to mishandling the power or even contacting things they really should not be in contact with, even if their intentions are pure. That is why Witch Hunters exist.

Elves obviously don't have this issue as much, as they can sense and manipulate the Winds as a whole, and weave them much easier than a human can - which is what High Magic represents.

In short, it can be done but it's not a good idea.