The simplest way to check if a tree is dead or simply dormant is to carry out a scratch test.

To do this, simply scratch back a small section of the branch with a thumbnail or sharp knife. It comes away easily. If underneath it is green, the tree is fine, and just needs more time and warmer weather. If it is brown, the tree is dead at that point. Sometimes the tips of smaller branches will die back, but the tree is OK. If you find a brown branch, move closer to the main trunk and repeat, and check the trunk itself. If you find green lower down, prune back to where you find green, and it will shoot from there. If the main trunk is brown, the tree is unfortunately dead.