Singleton LoggedUser class on Infrastructure Layer?

I'am developing an multi-layered application that suport many application UI consumers, like WinForms and MVC.

First, i'am developing a UI Windows forms to consume that.

I have the falowing project structure:

Application.DataAccess      - IUserRepository....
Application.Busines         - IUserService, ICustomerService...
Application.Infrastructure  - Logging, Exception handling... (Cross-cutting.)
Application.Domain          - Entities, User, Customer...
Application.WindowsForms     - UI

Most of my busines methods need User that has requesting like AddNewCustomer(Customer c, User requestingUser)...

I always have to pass Logged User through my User Interface application to Busines layer or should create a Singleton class on Cross-cutting layer and use that on all of my application?