I went to a foreign college on an exchange program through my university, would that count as having attended another college or school?

Where do you see this?  As add another 1098-T?

Who did you pay tuition to?  If you paid tuition to your US college for the exchange program, then no, it would not count as attending another school.

If you paid tuition to the foreign school and it is listed as a Eligible Educational Institution with the US Dept of Education, then your qualified educational expenses would be deductible.  If they are not listed, and you paid them directly, the education expenses are not eligible for any tax credits and do not need to be entered on your return. 

Simple answer: No. 

But, if you are wanting to claim tuition paid, separately, to the the foreign college, then answer yes.