Many Rainmeter skins today use the Yahoo! weather feed, and in the last few weeks these have become entirely broken or very unreliable. Sometimes they work, and sometimes they don't.
Yahoo! is in the process of changing access to their API query language (yahooapis.com) to require OAuth authentication to use it. WebParser does not support OAuth authentication.
So if you currently use a URL in your weather skin something like:
That is never going to work with WebParser.
You can change that URL to something like:
Which uses an XML feed that does not require authentication, however, I caution that using that has been shown to be unreliable. I don't know if they intend to do away with it, or if they just don't care that whatever other changes they are making is impacting that feed, but it will work some days, and not others.
I expect that many authors of popular skins will take steps to correct their code to use a different weather feed that is more reliable, but that is up to them. They might post a new skin / suite on deviantART in the next days or weeks, or may have moved on and will never revisit their code. There is a good chance that you will need to take matters into your own hands.
One thing you might consider is changing your skin to use the WXData weather feed from Weather.com (The Weather Channel) My experiences with this feed have been good, and I have no reason to think that Weather.com is going to stumble into the La Brea Tar Pits, as Yahoo! has done. I don't think you are going to be interested in the scraps of bone and entrails of Yahoo! that the predators are going to leave behind. It's time to move on...
It won't be trivial to make a change from one weather feed to another in a complicated weather skin, but you might take a look at Weather Skin Tutorial to see how you might get started.