Most visits to an employer's headquarters are done on a B1 visa.
The rules say that you cannot do work on such a visa, and that is true. But immigration takes a fairly narrow view of what is "work". You can:
Go to meetings
Plan your work
Get direction from the CEO about what you should work on
Discuss your work
Present the results of your work
There is no such thing as a business or tourist Schengen visa. In principle, there are only two cases:
If your visa is a single or double-entry visa, it's tied to a specific trip and should in principle have a short validity. Once you have completed your trip you can apply for another visa.
If your visa is a multiple-entry visa, it does already implicitly ...
Arne is right. Snowy, muddy or any other forms of shoes are not used inside private houses at all. We wear socks or a type of slipper. Inside a business, shoes that are clean enough can be worn, but you will find mats at the doors or just inside to wipe off excess muck. You will not have to worry about feeling cold even in socks, as all places are heated, ...