What you want is pretty easy to do, and the code exists already. But the way I invision it, you won't connect the sensor Arduino to your wifi. Instead, you'll use another Arduino as your gateway like this:
Sensor Arduino: Located outside, connected to temperature sensor, wind speed, rain gauge?
Gateway Arduino: Located inside, w/ Wiznet 5001 ethernet shield
The Sensor Arduino and Gateway Arduino talks to each other using a VERY easy to use wireless transceiver, nRF24L01+. The wireless modules are $3 each, and the library for use is very mature. All the sensor data is easily communicated to the Gateway using this library.
The Gateway Arduino w/ the ethernet acts as a webserver, enabling any computer in your local network to open up a page and view current conditions. Look at this page for the Arduino code:
You want to also save historical temperature/wind speed information right? This is the best part! The Gateway Arduino can push data to a service like Xively, a free web-based data collection service that also gives you a nifty way to visualize/graph your data. There is a little hiccup with using the Wiznet along with the nRF24L01 module. The wireless module and ethernet shield both use the same bus to communicate, so take a look at this blog to see how you can use both at the same time:
Xively also lets you make that data public or private, so you can chose to contribute your weather station data to the community.
Some other notes:
I like nRF24L01+ modules because they're dirt cheap. Xbee modules cost more than the Arduinos themselves. You can keep adding nRF24L01+ modules around the house once you establish a gateway. The same cost problem exists with wifi shield - expensive.