Lots of things you need to consider here. I'll relate an experience I had in a minute after a few things here.
First, what are the runway dimensions? Long runway, wide, or short and thin? Grooved, or not? Large airport with various runways, or just one single runway for arrival? I'd consider landing with poor braking action on a 10,000 foot x 150 foot runway if my alternative was fair braking action at the alternate with a 5000 foot x 100 foot runway. Also, how are the other weather conditions? Good visibility? Snow? Low ceilings? I'd consider better visibility, calmer winds, and no active snow/rain to come into major play here. I'd rather not land anywhere with poor braking action with a tailwind or gusty crosswind conditions that might create directional control problems.
I wouldn't make this decision on short final. I'd just go-around if I had the fuel available, and analyse the situation more. Where is my alternate? What other alternates might be available?
Key is not to be unprepared for a decision like this. If you know it might be "iffy" for landing, have some other plans of action in mind. Get weather reports from nearby airports. Find how much fuel it will take to divert. What airports are open, closed, etc.? I'm not sure how the military does it, but we practically get a book with METARs, TAFs, and NOTAMs for surrounding airports. I'd take a look at these and see what might be a decent alternative. Don't rush, but don't waste precious gas.
Now a personal story: We were flying a long leg into TUL one night, which was reporting very gusty wind conditions and turbulence. Good visibility. Alternate was west to OKC. Previous aircraft were diverting to XNA, only 10 minutes away.
We ended up getting a windshear caution on short final and had to go-around. We had decided to follow another company aircraft to XNA, after pulling up the weather on ACARS seeing 13 knot winds compared to OKC with 20G25 knot winds. Figured OKC was in the same boat as TUL with the front moving through.
What we didn't realize is we were right at the edge of the front. When we got to XNA, there were some scattered rainshowers around the airport causing heavy rain on final, and the winds were picking up to 25 knots and gusty. We bumped down final with dwindling gas in rain and lightning nearby hoping not to get a windshear again.
Looking back, it might have been advisable to see the trends for OKC and XNA. XNA obviously looked OK, but was getting worse. OKC may have been getting better, and was only about 40 miles farther I believe for the diversion. Plus, it may have had better facilities and runway arrangement for us.
Don't just use basic information to come up with decisions. Use all info. Look at your Jepps, and see how large the airport is. Runway distances, facilities, and options nearby the alternate. Get weather trends. Look at the Surface Analysis chart, Radar Summary chart, and forecast wind charts for your Flight Level when you are getting ready to leave. Don't just rely on a METAR or TAF. They are only good for the 5 mile radius around the airport.
We made it safe to our changed alternate, but looking back I would have liked to have been more prepared and had more information available. Use all resources, like dispatch, ATC, and each other to come up with the more solid plan.
In my example, I don't feel we did anything unsafe, because we made the best decision based on the information we had available at the time after a three hour flight. This was gathered while trying to fly in moderate turbulence during descent as well. Plan early.
