I do volunteer work with a lot of young people. In my experience, they tend to look at individual issues rather than party platforms. On issues such as civil liberties, race relations, LGBTQ, reproductive rights, immigration, I agree they are more liberal. On other issues, including many on self defense and RKBA, more conservative.
Oh, and I always heard the quote as "if you weren't a liberal in your 20s, you have no heart. If you aren't a conservative by your 40s, you have no brain."