Should I get rid of these suckers?

They've been growing from stumps that the previous owner left ~8 years ago. A couple weekends ago I finally started cutting back some of the taller suckers as they were growing at a 45deg angle towards the house and over the deck. Should I cut them all the way back to save the big/old trees in this cluster? What's the best path for the health/longevity of these trees?
Snow is due to fall any day now, if more aggressive trimming is recommended, should I wait til spring? Thanks in advance!