You can prune out the dead wood at any time but any major pruning of living wood would be best delayed until early spring (February), after the danger of freezing temperatures has passed and just before the spring growth flush. There is no need to paint any pruning wounds.

The Spanish moss can be removed by hand at any time. Although it is not parasitic, large amounts of it can reduce the amount of light that reaches the leaves of the tree and this can affect the productivity of fruit trees.

The trees should be fertilized 3 times a year, spring, summer and fall.

See this fact sheet for more detailed information on making proper pruning cuts:
http://edis.ifas.ufl.edu/hs121