Given my knowledge of the state it would seem unlikely but opportunities do crop up and you need to be ready to pounce. A good bet would be to find a small, not very well known lake/large pond/creek with an older, established neighborhood. In order to stay within your budget You may need to start with something other than a "small cabin" on a lake. Maybe something small within easy walking distance of lake access could be an option.
Look hard, thoroughly and persistently. Educate yourself about the areas you would consider. Subscribe to local realestate search engines that will automatically update you when something is newly listed. Network with realestate agents through their websites but do not enter into any written agreements if you can help it. I do not trust dual agency particularly as a buyer. Have your financing (buying power) in order as this is good leverage when golden.
When you do find something that will work for you, negotiate something. One easy thing to do is offer a quick settlement if you can in order to get a better price. It is a good time to buy as lots of properties are flooding the markets. Good waterfront can be difficult to find but being poised and prepared to move fast is a key.
Don't give up . . .