Well, some sad news, I figured out why there aren't many snow cone stands already in Houston. I haven't had any luck getting ahold of the right person at the health department, but from reading around a lot on their website here's what it looks like:
In order to use a "mobile unit" like a truck or trailer, you are required to make a trip to a commissary every day. You are required to store all perishables in the commissary and empty out wastewater and fill up supply water. The commissary will charge a fee, and while I've heard anything from $200-1000/month depending where I look, the idea of driving my ice trailer to a kitchen to empty out a water tank and move a few hundred pounds of ice every day is pretty unappealing for this size/scope of a business.
In order to have the unit at a permanent location hooked up to electrical or other utilities full time, it has to meet all Houston building codes, which a mobile trailer will most likely not do.
The other option is to rent a physical location, which is what Bahama Buck's does. In this case the one quote I got was for $2000/month for a location that isn't particularly high traffic, and isn't ready for any sort of food service. Of course this will change depending on the specific location, but I don't think I'll be getting much cheaper than that in the area I'm looking.
My $20,000 semi-passive investment idea is quickly turning into a $50-100,000 very active investment idea. I'm guessing a lot of the food trucks I see are just operating without the proper permits and are banking on the commissary rule not being enforced. Since I'm trying to put this in a high traffic location I'm not really interested in skirting the rules. Some of the food truck parks probably have commissaries really close by that prevents them from having to move, but in Houston those places have pretty limited traffic and are quite a ways away from me.
Luckily I haven't hit the order button on anything yet, although I do have an inbox full of price quotes and answered questions about trailers, ice shavers, flavors, etc. For now I'm going to slow down until I'm able to confirm what I said above with the right person at the health department. So far I've only been shuffled and transferred between people, this will be my 4th attempt to call them.
I guess the semi-permanent shaved ice trailer from my home town run by high school kids isn't really applicable in the big city, at least not Houston. It seems like such a simple concept, but I guess a few poor food handlers ruined it for the rest of us.
The search for a low startup business continues.
edit: I looked at the rules for Austin, and they allow you to empty your wastewater and transport it to a processing facility for disposal, or hire a service to do it for you. In Houston it's specifically required that you move your entire truck/trailer to an approved commissary to dump out the 30 gallon grey water tank that may or may not be full every 24 hours. I get the feeling some lobbying by brick and mortar food operations may have played a role in this rule. Basically it puts a stop to my idea until I leave Houston. I'm still going to try to get ahold of the guy at the health department to confirm all of this.