My neighbor said this is the time to trim back all the roses so they aren't long and spindly later on. I'm a rose newbie. I've been so happy to see all these new buds and growth on the roses I have... do I really have to cut them all way down???
Not all the way. In general, for hybrid teas, to knee height. For climbers, you want to keep the long arching stems but cut back the side branches to one or two nodes.
Check with your local nursery or the Portland Rose Society - they probably have free rose pruning classes going on right about now. There are many different types of roses and each is best pruned slightly differently.
Paul Zimmerman (formerly of Ashdown Roses) has some great, practical videos on YouTube with a lot of good pruning information.