I am interested in summitting Breithorn this winter (late January) using crampons and an ice axe. I am in excellent physical shape but I do not have much alpine experience. I have seen mixed reviews about whether or not I should hire a guide, but most companies do not offer tours in the winter. I am curious why this is the case and if I should even think about summitting Breithorn in the winter, and if I should even consider doing it by myself.
I do not have much alpine experience
Climbing the Breithorn in the winter is a much different matter than in the spring or summer. Any 4,000 meter peak in the alps is subject to arctic weather conditions with high winds and temperatures far below freezing. There is also going to be very deep snow, so unless you know how to ski or snowshoe, you are going to have a rough time even getting to the real start of the climb. If you've never tried to travel on foot in 2 meters of soft snow, you have no idea of how slow and exhausting it is. On top of that, a 35 degree slope is going to have significant hazards from avalanche. Until you have enough experience to evaluate the local avalanche forecasts and compare them to the conditions you actually see, you should be very conservative in your winter travel.
That being said, the Breithorn is considered the easiest 4,000 meter peak in the alps, but it still involves glacier travel and somewhat steep (35 degree) snow slopes. That makes it an excellent choice for a beginner (with a guide if you're a real beginner) in season (spring and summer).
As a general rule, I think it unwise to attempt, solo, for the first time, the sort of climb that one has no experience with, especially if it carries the potential for a serious accident.
You have winter against you, ice against you, inexperience against you, and possibly an unknown reaction to 4,164 meters against you. Solo? No, not unless your meaning of do not have much alpine experience is an extremely modest understatement.
As for hiring a guide, it is likely that a company will be able to find a guide for you, even if they do not regularly offer tours in the winter. You will be hiring a private guide and it will be more expensive than the summer tour. The reason that the companies do not offer regular tours is probably because there are not enough tourists who are able to climb a mountain in winter conditions.
Breithorn Ascent says:
This tour is a perfect way to get a sense of high Alpine air for the first time but only for surefooted and experienced mountain hikers accompanied by a mountain guide. The tour includes climbing a glaciated four thousand-metre peak, and this is not to be underestimated
•The overall difficulty of the tour is given as “L” (easy)
•A mountain guide is recommended
•Warning: glacier crevasses
Crampons, climbing harnesses and helmets can be rented in different sport shops in the village
This description and caveat is for a summer tour.
Don't try it. The (walking) mountaineering season is over, there is now too much snow in the high mountains and it definitely will not get easier till January. You have to wait until the Summer when the snow starts to get more compact. An early date for a 4000s ascent is June.
For mountaineering now you either need skis that carry you over soft powder or a much steeper wall where the snow will slide down before it gets a significant builtup. But then you are into ice climbing and the standard Breithorn route is far from this ;)