One could do an awful lot by SMS (including weather radar images) and I know various people have looked into this, but as LH2 says one needs to set up an account prepayment system, and the market is probably very small.
One can already get TAFs etc by SMS. Not sure how it's funded - perhaps the ougoing (request) SMS is to a premium rate number which then funds the return message?
Remember that a WAP facility for weather is free.