Yes, a stock VW, Air cooled flat 4, horrizontally opposed, just like whats in the vehicle will bolt right in with limited modifications. The only real headache you'll have is with the heater boxes. Your machine has what's called a "Stale Air" heating system. None of the Stale Air exchangers will fit on the later engines. The 1200 CC, 35, 36 and 40 HP variations all had small manifolds, usuall a 28 PIC carb, and were produced up into 1965, then the 1300 was only produced in 1966, follwed by the 1500 for a couple years and finally a long run of production as the 1600. It's all in the "Idiot Book". Definately a worthwile investment for anybody with anything VW powered.
Other later VW water cooled engines will also 'bolt-in' with limited headaches.
The 1192 CC, that you have is quite tempramental about cooling. All the tin needs to be in place and the spark and fuel/air ratio setting are quite important. Even the later "13","15", or "16 hundreds" as they are reffered to, will overheat and eventually breakdown if you don't pay attention to the operating temperature. The vehicle originally had a dipstick oil temperature sender. IF it's not there, or broken you definately want to replace it or repair it. Once it gets too hot it will boil the gas in the gas line and vapor lock. You'll have to open the hood and let it cool off for a bit to get it to start back up. There are a series of articles in this forum that will give you more details about this. Fuel is going to be your first problem and there are some suggestions about that too. Just about every question you could ask about an ST4--AKA--Snow Trac has been discussed at length in this forum. The answers are all there you'll just have to hunt around a bit. All the details about 6 Volt/12 volt are covered in detail too. Westermaskiner, the original builders, used 6 volt engines, with 6 volt flywheels and 6 volt starters for many years after they changed the rest of the machine to 12 volt. The transition occurs about 1966, the same year VW up-graded their vehicles to 12 volt.