I would prune them as soon as I noticed them. It's not like pruning a normal branch where sometimes, with certain trees that "bleed", you wait until times of the year that is less of a concern. With suckers, they are better off removed asap.

Are these all suckering, or are we really talking about water sprouts. If you have pruned them and gotten a bunch of watersprouts, you are likely to be pruning to much.

Suckers come from roots. Watersprouts are similar vigorous, mostly unbranched (at first) vertical shoots often produced in response to numerous or otherwise disruptive pruning of branches. The tree is hurrying to put back the crown portions that were cut away.

bboy, does it matter when it comes to the timing of removing water sprunts and removing suckers?

I only ask that question,because a 3 foot tall single trunk Yaupon Holly tree I planted not to far from the Northwest corner of my house did well for about 2 months after I first planted it in the late Springtime this year, but mid July it's leaves started going brown. Once I saw that I began watering it more often, and it slowly began producing new leaves.

The number of these leaves are increasing more now, since the daily hi temps have cooled and more rains than usual occured in late August. But the struggling tree did send up about three water sprouts with red leaves over that rainy period in August. I left them alone for a few weeks, but did remove them yesterday.

Was that wrong to do? I only did that in the belief it would prevent those sprouts from stealing water and nutrients from the tree's already well developed branches and new hardening off leaves.