I have to assume you meant no TAF on field, not no weather reporting station.
You use the FA as your forecast source; and what does the FA always say in bad wx? VIS 3-5SM. The FA covers your forecast requirement. Definitely check for alternate airport minimums before using such an airport as an alternate. Even if you can use it as an alternate w/o a TAF, you would check all area METARs and TAFs to get an idea what you're getting into. Part 91 makes a lot of flying legal that 121/135 restricts.
All the alternate airport filing requirement is for is to have some sort of plan before you blast off in IFR. You're not required to fly that approach or even land at your alternate. The METAR determines IFR/VFR (and for you Part 91 guys, you can even start the approach and determine for yourselves if you have the required flight visibility to land, but a favorable METAR can keep the administrator away).