Donsa asked the more relevant question. Why, if the approach is below minimums, would you initiate the approach to begin with? We enter into the miraculous to merely fly an instrument approach proceedure...we fly blind to a spot near the ground, and then land. But why would you elect to do so knowing that the minimums did not exist...why would you choose to fly to a spot near the ground, unable to see, when the very minimal visibility required for this great feat is known to not be available? Seems to me a lot like running onto a highway blindfolded, knowing there's traffic, in the hopes that it will be gone when you arrive.
Having so said...you ask if upon arriving at DA we find the approach lighting visible...do we continue? In accordance with 14 CFR 91.175(c)(3)(i), descent to 100' above TDZE is permissible with nothing but the ALS. As you're at DA/DH with the ALS in sight, is there a reason you won't be continuing?
This is up to you. If you're continuing and the visibility is indeed below minimums, you're setting yourself up for a hazard, as well as a potential violation on several counts. You can always say that flight visibility was adequate, but with the availability of official weather, in the event you cause an incident or accident, you stack the deck against yourself.
There are legitimate times when one might consider an approach under Part 91 when weather is reported below minimums...the most obvious to me is a time when it's clear and a million, you can see it, and know that the transmissiometer is frosted over or a reporting error exists. Other times with changing conditions, one might expect it to improve...it may have dipped below just as you began the approach, for the fifth time in the last twenty minutes. But generally, if it's that low, you probably shouldn't be wasting your fuel when you could divert to a place that is above minimums.
If under Part 91 you're carring enough fuel to blast away all day at that approach with abandon, then have a ball.
