I am usually pretty good on the internet but I cant find anything telling me what models and brands of snowblower I can use with my 3813 tractor. Can anyone give me a list of what I can look for and buy?
Honda attatchments are really rare now since they are no longer made, but they still come around once in a while. My best reccomendation would be to keep an eye on Craigslist or eBay, or make another brand snowblower work on your tractor. I don't know where you are located, but I was able to find a single stage snowblower for your tractor in MN though the price isn't within a reasonable range. Like I said, it may be easiest to have a machine shop make the nessecary changes to another snowblower to make it fit, because you will likely have a VERY tough time finding what you need for a reasonable price.
Honda did offer a single-stage snowblower for the HT3813 lawn tractor. It was called "Snow thrower kit, HT3810-ST" It has been out of stock since 1990, according to the parts system list. I found a single drawing of it in a catalog from 2001. There was also a dozer blade for that tractor too. Even if you could find all the individual, loose parts to build one, it would be VERY expensive.
But, might want to set-up a google-alert for HT3813, HT3810, snow and you never know what might show up one day.
Caveat: I work for Honda, but the preceding was my opinion alone.