As you have a rug for her, she might be OK with a bib clip. Does she sweat at all when you ride her during the winter? If not she will probably get away with not being clipped. If she's part or full thoroughbred, she really shouldn't need clipping as they tend to have very thin coats. My boy is 3/4 thoroughbred, and he isn't clipped.
If she happens to sweat quite a bit, particularly around her girth area, you could possibly get a low trace. For a horse in very light work in the winter, I wouldn't clip any more hair off than that.
As for the issue about her never being clipped before: Most horses don't like being clipped. The majority will tolerate it, but it doesn't mean they like it. She may be OK with it, or she might not. We don't know your horse so we really can't tell you. You can how ever use a twitch on the horse whilst it is being clipped. If you don't no what it is, it basically involves a loop of strong rope on a stick. The loop is wound around the upper lip tightly and it does cause the horse minimal pain. Enough to keep its mind off the clippers. Be aware that this is a little cruel, and sometimes the horse will rear if it has the twitch on too long. I personally don't like this method. I prefer sedation. This is another option, if your horse hates being clipped. You can get the vet to administer a weak sedation, to make the horse drowsy, and prevent it jumping around all over the place.
Here are diagrams of the bib clip, the low trace and the twitch, if you are new to any of this :)
The twitch can be seen best in this picture :)