Doing peaks in snow/calendar winter is very different from your typical summer hikes and there is a lot more than meets the eye.
There is no way a single post can prepare you for everything, but there are some good starting points and/or prior threads to help you research and figure out if you want to get into it more and to what level.
The single biggest piece of advice I can give you is
don't skimp on your research. In winter, there are so many more variables to take into account on a hike/climb. A mistake is much more likely to have very serious consequences.
First peaks: Start very easy. Like anything, you want to build up to doing some of the peaks in winter. Quandary via the East Ridge, Bierstadt via West Slopes, Bross and Lincoln via Moose Creek, Sherman via the South Slopes are good, fairly safe places to start. They all have fairly safe and gentle terrain and hopefully you've already done them, so they are familiar to you. Also take a look at this article from our own SurfAndTurf for some good pointers:
https://iceandtrail.com/2015/11/11/5-wi ... beginners/
Gear: Getting a solid gear system down can take awhile. Everyone is different, so work on figuring out what works in given conditions on a peak like Quandary where if something isn't working right, you can get down to the safety of your car quickly. A lot of winter gear is all about layering properly and not getting warm enough to sweat. No need to invest in mountaineering boots right away. Warm hiking boots with good socks and gaiters will work well in decent weather for your first few peaks. That said, you will want traction to help on slippery terrain. Initially Microspikes are a great investment that will serve you well for a long time. Kahtoola is the gold standard. Don't bother with YakTrax. Crampons aren't something you will need for awhile, so don't worry about them. An Ice Axe isn't essential right away, but getting one and learning how to use it and practicing will be critical if you plan to do more than just very basic and easy stuff. (Mine has already saved my life once)
Education: Take an AIARE level 1 class as soon as possible. You don't know what you don't know...and taking AIARE 1 will really help you get an idea of what is out there and how to avoid the dangerous stuff. Even some of the "easy" 14ers have avalanche terrain that isn't all that apparent, especially to the novice. I strongly recommend Colorado Mountain School, but there are quite a few great organizations that offer AIARE 1 classes. Also look at attending a talk at REI or some of the other backcountry retailers on winter hiking.
Experience and partners: See if you can get some fairly experienced folks to go out with you early on. There is no substitute from learning from more experienced folks. That said, consider attending this years 14ers.com Winter Welcomer. It's a annual event we do on Quandary Peak around Halloween and it's specifically geared to help give people new to winter conditions experience. Here is the thread from last year's event along with pictures:
https://14ers.com/forum/viewtopic.php?f=5&t=50705
Hopefully this helps give you a good start.
-Ryan
"Climbing mountains is the only thing I know that combines the best of the physical, spiritual, and emotional world all rolled into one." -Steve Gladbach