Does it matter that I don't attend the university for which I'm looking for research?

I'm a first year student looking for some research opportunities this summer, and the commute between my home address and my uni is 4 hours; ideally, my summer research is in my home town (there are a few universities in the area). Do undergrad labs care that I attend a different university from their own? If so, how can I re-word my cold emails to better compensate for this?