You should remove dead branches down to just above a node in the still living tissue (if there is any). You can do that in spring (there's some risk to pruning in fall because the dampness of the weather etc. may allow fungal diseases to get started). Whether you can cut living branches right back (to above a node) in fall would depend on the hydrangea. Some you can cut back in the fall or spring because they form flower buds on the new growth. I always do those in spring if they need it. Others form their flower buds the year before so if you cut back all branches in spring or fall you will not get flowers for a year. If you want to prune any shrub that flowers on old wood you should do it right after they flower. Do you know what kind or cultivar of hydrangea you have?
