Many plants, including holly, undergo a dormant period during the winter. While it is not necessarily ideal to prune them during this time period, we can say this much with certainty: that it is, at least, safe to prune them at this time.
When you winter-prune a shrub that blooms on old wood, in doing so you are potentially cutting back on the number of flowers that will appear on the plant during the following growing season. The trade-off is sometimes worthwhile because you are choosing a time to prune that is safe for the plant. At other times of the year, pruning may leave the plant vulnerable to diseases or spur new growth that will be damaged by frost.
Holly is one of the shrubs that blooms on old wood. Any floral buds (whether on a male or female holly shrub) located on the branches you prune off in winter are buds that will not open during the upcoming year, resulting in reduced pollination and fewer holly berries. We typically prune flowering shrubs that bloom on old wood in spring just after the blooming period is over. Holly is a bit different since we are not growing it for its floral display. Nevertheless, if safeguarding berry production is a priority for you, you could certainly wait until your holly has flowered and begun to form berries before pruning. Just remember not to prune too late in the summer, because you could generate new growth that would only be killed in the first frosts of fall.
Indoors or Outdoors
Part of the fun of growing certain kinds of holly shrubs is in admiring the berries. If you have such a shrub and it is covered in berries come December, would you rather leave the bush intact during the holiday season or bring some branches indoors to decorate your home?
Some people prune holly in early winter since they wish to bring the trimmed stems —with their holly berries—inside for the holidays. Others prune holly later in winter because they prefer their display of holly berries outside. That part of it is up to you, since, either way, you will be pruning at a safe time, when the shrubs are dormant.
How to Prune Holly
When pruning holly, use bypass pruners, not the anvil style. You should always remove dead, damaged, or diseased branches whenever you find them, and it is generally advisable to cut off a branch that is rubbing against another branch or jutting out in such a way that it spoils the overall appearance of the bush. Beyond that, holly is too diverse to give a general answer to this question, so here are some examples.
Blue Princess Holly
Blue Princess holly is one of the Meserve hollies. It is a shrub with red berries and dark-green, prickly leaves. You need to get in there and prune this type while it is still young in order to give it a sustainable shape that you can then maintain as the bush ages. If you skip pruning for a few years while the plant is still young, you may end up with an unmanageable plant later. Once you do attain a desirable shape on this shrub, it is best to prune sparingly; tip-prune it to maintain shape wherever possible. If you do need to cut further down a branch, be sure to make your cut right above a leaf bud. If, on the other hand, you are forced to perform a drastic pruning on this bush, be prepared for it to look unsightly for a long time.
Hetz Japanese Holly
Hetz Japanese holly is that type of holly that you have mistaken for a boxwood shrub while driving through your neighborhood and inspecting your neighbors' landscapes from a distance. Different from Blue Princess, it has tiny leaves that are not prickly, nor is it grown primarily for its berries. Unlike Blue Princess, it is very easy to prune. If you have disease problems with yours, you might want to open up the inside some by making thinning cuts; this promotes healthy air circulation.
Sky Pencil Holly
Sky pencil is another Japanese type, but it is valued for its oddly narrow plant form, and like Hetz, it is easy to prune. Depending on your needs and desires, you may not even have to prune it much at all. Pruning should be minimal unless your bush suffers severe damage from snow and ice build-up. The latter can be avoided by wrapping twine or bungee cords around the shrub to pull the branches in tightly toward the plant's center.
Inkberry holly is another no-fuss kind of holly; again, something grown as a foliage plant with berries being just a bonus. That quality is precisely why you see mass plantings of it in public places, as it is easy to maintain. Prune simply to thin, shape, and control its size.
Holly also comes in tree form. American holly and Nellie Stevens holly are examples. You can shape a holly tree to your tastes by pruning, and some people cut off some lower branches to expose more of the trunk. If you do not want your tree to get overly tall, you can prune back the leader every winter. Be sure to make your cut right above a branch with some good, vigorous green growth on it, because this is your new "endpoint."
Unlike the kinds of holly presented above, winterberry holly is not evergreen. It is so different from the more typical hollies that we might as well be discussing another plant altogether, especially when it comes to pruning. While drastic pruning is a bad idea for evergreen hollies, it is quite acceptable for winterberry, which responds well to rejuvenation-style pruning. Remove up to 1/3 of the stems each year, targeting the oldest, thickest ones.