Will ClickOnce be ported to .NET Core 3 as well as WinForms?

Current status

It appears that ClickOnce won't be ported to .NET core 3, but will be ported to .NET 5 as per Matthew Steeples' answer below.

Original answer relating to .NET Core 3

Microsoft's Scott Hunter addressed this in the comments of the .NET Core is the Future of .NET blog post. He was asked:

What about ClickOnce? Will that be a supported distribution system for .NET 5 desktop applications?

To which he gave the response:

We are going to recommend MSIX for installation and support for MSIX will be added for Windows 7 so it should work on all the platforms you that .NET Core runs on.

More details MSIX can be found in Microsoft's MSIX documentation and in it's GitHub repo.

Other installation frameworks exist too, such as Squirrel.

There is no mention of anything about .net core 3 winforms working with Clickonce. The answer provided above had a link that had Scott Hunter who redirected to Microsoft's MSIX technology. Based on my readings the only way to deploy to end users without using the Microsoft store is to "sideload" your application and that seems to involve many steps that may make the user hesitant even if you sign the package it seems that users have to enable sideloading first. Not my idea of user friendly.

All other answers answer the question for .NET Core 3, but this is changing for .NET 5. Microsoft are providing support for ClickOnce as described in this GitHub issue (July 20th 2020): https://github.com/dotnet/deployment-tools/issues/9

It's not full support (ApplicationDeployment class will not be available) but it's a start.

It looks like it's going to be available as of RC2 - https://devblogs.microsoft.com/dotnet/announcing-net-5-0-preview-8/