Winter is the best time to transplant small oak tree seedlings as the trees are dormant. Oak seedlings must be under two years old for a successful move as the taproot on older trees is too deep to be excavated. If the taproot is severed from the tree, the seedling will die.
Dig the transplant hole prior to excavating the oak seedling from its current location. The seedling is best removed from the ground when all leaves have fallen from the young tree. According to Douglas D. McCreary of the Integrated Hardwood Range Management Program, the new transplant hole should be at least two times the size of the estimated root ball on the young seedling. In this way the taproot will not be folded over. Loosen the soil inside the new transplant hole.
Remove the transplant oak seedling from its current location. The height of the tree and the trunk diameter will give you a good indication as to how deep and wide the root ball must be dug, according to the University of Iowa's Forestry Extension. An oak's taproot is a third to half the overall height of the tree. In other words, if the oak seedling is 2 feet tall the root ball should be at least 18 inches deep. Make adjustments to the transplant hole as needed.
Set the transplant into the new hole. Align the topsoil line from the transplant to the current soil level of the new transplant area. Back fill any loose soil around the root ball.
Water in the new transplant with the garden hose. Add at least 10 gallons of water to the new transplant to remove any air from around the root ball.
Install a wooden stake next to the new transplant if winter weather may cause the upper small trunk to tip over. The transplant may also be weakened by the move. North Dakota State University Extension Service recommends using a piece of twine to tie the trunk to the wooden stake for extra support. Do not place the wooden stake right next to the oak seedling transplant. Instead the stake should be well away from the new root ball of the seedling. If need be, install the wooden stake at an angle to meet the top of the new oak transplant.