There are no legal constraints to deploy, distribute, sell or give away applications you have created with the .Net framework, whether in C# or VB.net even if those programs use WinForms (or aspx for that matter). You could license such applications as you see fit, be it under a closed source license or open source software license.
You could develop such apps without an IDE (although it could be argued that it would be less productive). The reason you are paying when you buy Visual Studio is for the tool itself, which in my opinion is quite good, not to have some right to distribute your apps.
If you do not want to pay for Visual Studio or work without an IDE, there are alternatives like you mentioned; MonoDevelop, SharpDevelop and Visual Studio Express being some of them.
Regarding the purchase of the license
On another note, I noticed you mentioned the client is not willing to pay for Visual Studio licenses.
Unless these are out of the ordinary or very specific, I would expect an independent contractor or a software development company I would hire to develop software to provide it's own tools like Visual Studio or Resharper. I say that as an independent contractor myself.
Of course, I do not know your specific situation. You may be working integrated in the client existing team and required to use his hardware and software. In that case, disregard this last statement.