There are low-power WiFi modules around, like the Gainspan ones:
https://s3.amazonaws.com/site_support/uploads/document_upload/GS1011M-PB.pdfBut it would need someone with some electronics development expertise to build a unit based on something like this (there are other makes too), work out how to minimise the current drain and then build up the unit into an overall sensor/transmitter package which is properly weather-proof and capable of robust, long-term operation in adverse climates. It's not really enough, other than proof of concept, to demonstrate that such a unit will work under favourable conditions - to be considered a 'proper' serious weather station, it has to be deployable at most locations worldwide and deliver eg at least a 5-year service life.
I did look into this a year or two back, can't find the detailed notes right now, but IIRC what made these modules low-power (beyond careful circuit design) is that they were specially configured to be able to use a low-power sleep mode, but from which they could wake up,
quickly reconnect to the network and transmit a data packet before sleeping again.