Snowmobile tags on lakes?

If there is not any visible sign or border that denotes snowmobiles it should not cover any area. Since the Scandiavian laws are build on Allemannsretten your IMHO to go anywhere with respect.

A duplicated natural=water area won't work as expected. Imagine there will be some service for displaying or searching of water areas suitable for snowmobiles. It will then have two contradicting results for this lake.

In my opinion the ways in question needs to be removed and the snowmobile tag has to be added to the "real" natural=water way. I can't imagine some parts of the lake are allowed and some aren't, at least not in such a strange manner as shown in the screenshots.

I did not think one second that the snowmobile=no polygon was innacurate, coming from a very bad mapping day, a particularily dry winter, nor a clumsy import :-)

If I'm right and Hendriklaas wrong, then it seems that snowmobile are forbidden only in the area mapped as such. The question is then, do we need to add a tag on the limit from where snowmobile usage is restricted ?

Thanks for the comments. Yet, I am missing the answer. IMHO adding highly specialized tags (like snowmobile, or piste as is done here https://goo.gl/oD2cZe, and so on) to overlapping lakes is wrong, even damaging and unfair practice. There are many reasons for saying that. For instance, the OSM wiki says that these tags may be added to tracks and routes (line objects). Much worse, geometry parameters of these speculative areas perfectly mach the parameters of a huge number of wrongly tagged islands as lakes over lakes.
So, map/makers have two options: render lakes over lakes (and miss huge number of islands) or make holes for the overlapping smaller lakes (and creating some virtual islands). Obviously, both options are wrong. Therefore, to help the GIS and map/maker, the local community/mappers should correct this mismatch and avoid the practice.