I have a customer who wants an application for his travels where he can update an online DB, he doesn't want to buy a laptop, he wants a tablet or something similar. I have no knowledge nor desire in creating special apps for mobile devices, I want to create a winform just like I always did when it was targeted for pc. Tablet pcs (which from what I understood is just a regular pc?) are still very expensive in my country.
Is there a simple adjustment to make winform app run on a tablet with android or I have to build a special app for it? Any other solution? (I began in writing a web page for it, but it's much easier using winforms)
Native WinForms applications will not run directly on Android (or any non-Windows platform). You may want to begin by looking into MonoDroid for porting .NET code Android (and Mono in general for porting .NET code to non-Windows platforms).
A successful port across platforms will require that the application be structured in a very de-coupled manner. Core business logic in the abstract part of the application should be easily ported, but concrete implementations (specifically views and data/service access) will require some re-implementation for the different concrete platforms. So the overall architecture needs to be very de-coupled and pluggable.
Is a Windows tablet an option? Using various new technologies at Microsoft (Windows 8, Metro UI, etc.) you could build an application that would target multiple Microsoft-based platforms. This could easily satisfy the requirement of being "a tablet" (if the requirement isn't more specifically "an Android tablet"). However, it won't be the old WinForms style of applications.
In general you'll find that the industry has been steadily moving away from WinForms for, well, this exact reason. It doesn't port to other platforms, and there's a wide variety of platforms in demand today.