There are two distinct issues to deal with in this question:
- The question of ohel due to the size of the hat brim.
- The question of wearing a hat that can be blown off and thus lead to possible carrying.
It is important to bear in mind that in both issues we are dealing with a d'rabbanan issue, which leaves us open to be more lenient than if we were dealing with an outright melacha d'Oraisa. (A hat is not considered a genuine ohel d'Oraisa (MB 301:152).)
Brim Length and Ohel
With regard to the question of ohel, the first issue to deal with is the length of a tefach. According to the handy little chart in the back of R' Aryeh Carmell's סייעתא לגמרא, R' Moshe Feinstein holds a tefach to be 3.5 inches. (The Chazon Ish holds about 10% longer, and R' A. C. Noeh holds about 10% shorter.) (Moreover, if I understand the halacha correctly, the issue is not the actual length of the brim but how far it extends from the head. Thus, a curved brim will be significantly shorter than a straight brim.)
While it is perfectly possible to get yeshivish black hats that have brims that are well below the length of a tefach, hat brims that are more than a tefach are apparently quite common and popular in the frum world. This therefore does raise a serious question.
The Mishneh Berura (301:152) discusses the question of hats of this sort that were commonly worn on Shabbos, and cites a variety of different justifications for the leniency. Although not all of these explanations would apply to modern fedoras, the most basic answer is that people rely on the opinion of Rashi that there is no prohibition of ohel with regard to hats in the first place. Thus, the MB concludes that in a place where people are generally lenient on this issue, we should not protest (אין למחות), however in a place where they are not accustomed to being lenient, it is certainly proper to be stringent.
So, with regard to ohel it would seem that there are certainly valid reasons to be lenient, but it would be best to just by a hat with a 3 inch (or smaller) brim.
A Hat that Can Be Blown Off
The issue here is that the rabbis enacted a decree prohibiting wearing a hat that can be blown off in the wind because if that happens we are concerned that the person will pick it up and carry it for four amos. In his discussion of this issue (301:41), the Mishneh Berura explains that this issue only applies to hats that are worn on top of smaller hats. The reason for this is that a religious Jew will not walk in public with a bare head, so there is no risk that he will inadvertently carry his hat for four amos after he picks it up if that is the only hat he is wearing.
This, of course, raises the question about our current practice of wearing hats on top of a yarmulka. If our hats qualify as hats that can blow off in the wind (and, in my opinion, they clearly do), then one should certainly avoid walking in a reshus harabbim with a yarmulka under the hat as the MB paskens. (This happens to be my personal practice. When I was a student in the Mirrer Yeshiva in Brooklyn, I observed that when R' Shmuel Birnbaum zatzal arrived for shacharis on Shabbos morning, he would walk to his seat with his hat on, take a yarmulka out of his tallis bag, remove his hat, and put on the yarmulke.)
Those who are lenient presumably maintain that, as a general rule, our hats are sufficiently firmly attached to our heads that they are unlikely to blow off from a normal wind. Of course, this would vary from case to case, so it is difficult to give an absolute rule.
Moreover, it would seem that this prohibition would only apply in a reshus harabbim d'Oraisa, which is fairly uncommon except in densely populated metropolitan areas like Brooklyn, NY.