The AspNetUser isn't stored in HttpContext.Current.User property. An IPrincipal object is returned by HttpContext.Current.User, and the only members specified on IPrincipal are IIdentity Identity and bool IsInRole. The IIdentity interface then provides you with the Name property, which you can use to lookup the actual user object with.
If you just want one line of code and have full access to the User object, you can access the AspNetUser with the following code:
ApplicationUser user = System.Web.HttpContext.Current.GetOwinContext().GetUserManager<ApplicationUserManager>().FindById(System.Web.HttpContext.Current.User.Identity.GetUserId());
You'll need the following using statements:
using Microsoft.AspNet.Identity;
using Microsoft.AspNet.Identity.Owin;
Just note that it's probably better to go through the UserManager API if you're able to, and once you have your User object, you can edit and then save changes via the UserManager update methods. Many changes can be made directly through the UserManager methods. If you have an instance of UserManager around, you can also access the User object by:
ApplicationUser user = await UserManager.FindByIdAsync(User.Identity.GetUserId());