Is there any way I can change the wind speed from miles per hour to kilometers per hour?
The wind speed unit is determined by your region settings. Depending on your original region you have to change from your region to a similar region using km/h instead of mi/h.
Example: changing the region from UK to Ireland will change the unit from miles per hour to kilometers per hour in Weather.app.
Changing the region settings is not restricted to Weather.app but will change things in all apps!
I will refrain from making jokes about proud Britons forced to use the Irish region settings to get a metric unit!
Edit: found a reasonable solution for the UK: English > Gibraltar apparently also uses km/h instead of mi/h (at least in iOS7) ;-)