Is there an impact on SearchEngine results if my hosting company is not in the same country as my customers?

example:
I am in Switzerland, my business is in Switzerland and my Customers are in Switzerland...
So I want to optimize my site for my Customers geo location.
What is the impact on my SearchEngine rankings if I use a low cost hosting provider in the USA... does this cause me to appear as though I am a US based domain / company?

Unlikely, search engines to the best of my knowledge do not take into account server locations vs. business locations , here in the US most websites hosting servers are typically in a different state than the original business.

The only issues you may have a server related because your server will be in a timezone different than you , your stats and other server time specific stuff may be different than you expect.

Search Engine rankings are goverened by two main factors, off-page (inbound links, link text, etc) and on-page (content, title and desc tags, update frquency etc.)