I've been giving some thought to this once again as I listen to podcasts from KnitPicks. One episode was geared to what one book has patterns that would satisfy most if not all of your holiday knitting. I think you would have to know what you are planning to do in the general for each person you are knitting for before you can start pinpointing patterns. One of the people quizzed said that she kept her knitting for holidays simple. Choose basic patterns that you can do easily but with enough variety to prevent boredom and let the yarns you choose carry the project. Another people quizzed said that you should pick projects based on the recipients. In other words don't give something lacy to a person who really only likes and wears tailored items, a bulky wool sweater to someone who lives in the tropics. However, you can give finger-less mitts to people who work in offices that are not heated as warm as our homes or feel so due to the sedentary nature of their jobs.
Today's patterns are all about finger-less mitts and mittens. You can choose patterns that use yarns as fine as fingering weight (sock yarn) on up to patterns that use super bulky. They can be knit or crocheted. Mittens are appreciated by almost everyone and they can keep your hands warmer than gloves by keeping the fingers bunched together.
Some choices for easy patterns would be
These are all from Red Heart. However, they were chosen for being easy to knit or crochet and allowing the yarn to give emphasis to the mitts or mittens. Any pattern you choose can be done in any yarn as long as you remember to check the gauge of the yarn recommended and match that up to the gauge of the yarn you want to use. As your math skills get better you can pick any yarn to go with any pattern.