Apparently, this is due to an update to the beta track of the Google app, which removed the weather from the widget. Many felt that it might be the January 2019 security update, but Google pushed out a new update to the beta version of its app at the same time – and that is the real culprit here.
Currently, the "At A Glance" widget only shows the date, without any weather information. It's likely not a huge deal, but it is a bit inconvenient to need to go open a weather app or switch over to the Discover page to find out what the weather is like right now. This is likely something that will be fixed in the next update to the Google app, but it does show that this update is clearly not ready for the stable version.
The quick fix would be to opt out of the beta of the Google app, and the app will uninstall the beta updates, bringing back the weather to your home screen. So if you are on that cannot wait for Google to update its beta version of the app and bring back weather, there is a workaround. You could also return to the beta once Google does straighten this out. You will also need to toggle location off and back on to trigger it to appear again on the home screen.
Now this is a beta version of the app, but it still goes to show how bad Google's quality assurance has been lately. Removing vital features of an app – even if it is a beta version – is not cool, and it's getting quite a few people upset. With beta's it is expected that we will see some things changing and some bugs coming up in these new versions, but seeing large features of the app being removed is a bit strange, and not common.
The Google app is responsible for quite a bit on your smartphone. It was designed to be able to control a lot of aspects of your smartphone, so that Google could push out updates fairly quickly to your phone, without needing to do a software update which costs much more and needs to be certified by the carriers before it can be pushed out. This app controls the Discover on the left of your home screen (if you are using the Pixel Launcher), it also controls some of the Google widgets, and the search on your phone. So it's a pretty vital part of your phone and to see how easy it is for Google to break features in it is pretty surprising.
Google should be rolling out an update to the beta app in the very near future to fix this issue. Though Google has not yet confirmed the issue, so you may be waiting a bit. The best bet is going to be to leave the beta.