racerone is right...it may need a carb cleaning.
Water CAN get in the oil....but I'm not aware of it being a prominent issue with these outboards.
Yes...NO oil filter. Well...there IS an oil filter in the sump but it is not serviceable unless you take the power head off of the oil case. That is something that I don't like about these outboards. After MANY years....the ones I've taken out and cleaned when doing engine work were pretty gunked up. I don't think Honda EVER expected these outboards to last as long as they have. But... they built them well and they built them tough!
One thing these are fairly notorious for is developing an exhaust leak at the manifold to head gasket. You will know yours is leaking if the engine tends to die out after a bit and then re-starts and runs ok for a while and dies out again. Well....you won't know it's an exhaust leak UNTIL you pull the engine cover off and the outboard runs FOREVER. That is the test: If it dies out running but then doesn't die out with the cover off....the gasket needs replacing.
Doing the gasket is "major surgery" but these are so easy to work on that most guys don't have a big problem doing it.
Replacing the exhaust gasket requires that the power head be removed from the oil case.
The good thing about having to do this "chore" is that it also allows you to rectify and prevent future failure.
Remember where I said to clean the oil filter requires removing the power head? Well this is the time to clean it! Also...there is an oring "nestled" inside a circle cut out of the oil pan gasket that seals the water entering the block from getting in the oil....the water in oil issue previously mentioned. Well, if you have to go in to fix the exhaust gasket and clean the oil screen....you will be replacing that oring and using a new oil pan gasket.
So, I have always looked at repairing the exhaust leak as an OPPORTUNITY to do some much needed PREVENTATIVE maintenance.
If you have to do it....and you have the WHOLE winter....it is not too hard at all.
Just be aware that there is a "hidden" bolt securing the oil case to the power head. If you don't get it out and TRY TO FORCE THE CASE AND BLOCK APART....you will CRACK the oil case! They are still available but at around $1000 us replacement cost....it pretty much makes your outboard toast. But if you DON'T FORCE anything...you will be alright.
Another thing that can be addressed is the oil filler adapter seal/gasket. It is another way water can enter the crankcase. Check out Items #15 and 16 in the link below.
http://www.boats.net/parts/search/Honda/Outboard Engine/0/BF100F SA/OIL PUMP/parts.html
What happens is that, over time, the plastic housing that is the oil filler "body" will warp. When it does....water CAN enter the oil through the poor seal at the #16 gasket. Just replacing the gasket will NOT fix the problem. It would be VERY WISE to replace the filler body and gasket if you have the power head apart.
Another issue you may encounter when pulling one of these apart is the erosion of the aluminum where the water tube connects up to the oil case. There is a BIG rubberized seal there but on engines that were used heavily in salt water...I have found the metal has suffered a great deal and a good seal can be impossible to obtain. UNLESS...it is repaired. I have carefully removed all of the oxidized metal in that area and applied epoxy to "reform" the hole for a good seal. So far so good. My first one was about 4 or 5 years ago and it is still holding. Hopefully...you won't encounter that little problem on your outboard. But...if you do...I'm here to tell you it CAN BE FIXED.
If you want to be fairly independent in your work....get the shop manual...it's not the greatest but it will tell you what you need to know. This one:
http://www.amazon.com/Honda-Marine-...s=honda+10+horsepower++outboard+repair+manual