I prune all my hollies (different types BUT all the same family) April for Hedging but for shrubs I want to shape ot keep to a certain size, I do that in July or August, that way, the tender new shoots have time to harden up before the winter.
Depending on the size of the plants / shrubs, it's best to prune with proper loppers as IF you use hedge trimmers, you clip lots of leaves in half or chop them up and later they turn brown though never damage the plants.
Variegated Hollies IF neglected sometimes revert back to their green state and you need to cut these stems / branches right back to the wood but, these type of Hollies need a good bit more sun the most other types.
At Christmas when you want Hollies wirh berries for house decoration, dont strip the one plant of ALL berries, take from several or it may take a while for the plant to flower and form more berries the following year.
Hope this helps you out a bit.
Best of luck and kindest Regards.