Pines and other seral (pioneer) conifers come up in numbers after clearing, in this case these are all seedlings. Most conifers do not sucker, this is much more prevalent among broad-leaved trees.

As Bboy says, if they are pines or other conifers, they shouldn't sucker and lopping them off near the soil surface should be the end of them. If they are broadleaved trees, some species may try to sucker, and some may try to send up new buds from the crown area at the soil surface. To prevent that, lop them off just below the soil surface so that you are cutting below the crown and getting a little bit of root. You could also lop them off near the soil, then immediately paint the fresh cut with full strength, concentrated (40+%) glyphosate.

Thanks to both of you two. They are mostly pines/evergreens, but there are definitely hardwoods. Many beech saplings with some other hardwoods. It is a comfort to know the pines won't suckle (is that a correct term?!) since there are SO MANY! Hopefully getting all the trees while they are all small will help things. I appreciate your input!

Deanna

Suckle - suck milk from the mother's breasts; of infants and baby mammals (Answers.com)

Beech will likely sprout as that was a common practice in the past in England (coppicing). Your seed bank in the soil may allow many seedlings to pop and release with the sun. some of them being hardwoods and some being conifers. Collect local seed only for your reveg - local meaning surrounding watersheds.

Dan