I have 2 degrees and will be voting out. My office has a very high proportion of degrees and all are voting out. The only people that have said they want to remain aren't British and so can't vote anyway. I have yet to meet a single person that is eligible to vote and wants to remain.
Lots of degree educated people in my team at work are leaning out. Those leaning in are the minority. I wouldn't want to extrapolate and assume though.
As always, polling data gives a statistical likelyhood. Individual anecdotes of the opposing direction are not an argument against.
Polling data - as the most recent election showed* - is not always correct but it's still a lot more reliable than drawing conclusions from your observations of what the people around you think. If the people in my circle of friends were representative, we'd have AV, had a Green-LibDem coalition in 2010, the Scottish referendum would have passed, we'd have a Green-Labour coalition in 2015 and this referendum would be an easy victory for Remain. Your personal observations are no more reliable a guide to public opinion.
* - Although it's wasn't nearly as bad as being made out, the polls were within 10% of the final vote shares - outside their expected margins but not hopelessly, desperately wrong.