I thik it depends of when you want to do that befor your application or after that
in my opinion it's better to find an adviser befor applying for uni itself especially for USA many of my friends could get scholarships,TA or RA this way and me too
but last year when I just send application materials to unis no one accepted it
many advisers accept studnets as their future students befor their admissions
so I strongly recommend you to do so,fisrt mail teachers and when they accepted you apply for that uni
hence the best time to do that is 2 or 3 months before application deadlines
in that time, most of teachers are aware of their grants and the potensial positions such as TA or AR
and be careful to mail advisers in a time that they see your Email on tops of other emails and check them
because many students send emails to them and they may not ckeck all of emails
(you can mail early inthe morning,local time of USA)
anothe important point is that don't mail; them using Yahoo or gmail or other free mails
if you have a mail account in ur uni it's better to use that to avoid spamming protection send your email to bulk
I should mantion that this email process recommendation works for USA not Canada
and forneither EU
in Canada they are very restrict to application process
and in EU you should first find a project in many countries and apply for that
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