I would like to use an iPad for preflight planning. Can I also use the iPad to check weather while I'm en route?
Can you? Yes, but service might be slow or spotty.
May you do so legally? That probably depends. The FAA doesn't specifically prohibit the use of any electronics in GA aircraft; they only state that under 14 CFR §91.21, those aboard an IFR aircraft can't operate electronic devices unless they are
It's possibly questionable that you as the pilot are an authority on whether or not your devices will cause interference.
The FCC, however, has banned the use of cellular phones in flight per 47 CFR §22.925:
Whether or not that can be interpreted to apply to an iPad's 3G connection is pretty iffy.
Unfortunately, in the US it is not permitted to use cellular service in flight because the FCC does not permit it.
On the bright side, the FCC just released a press release which says:
That being said, even if it might work at low altitudes, I would highly recommend against it if you are flying IFR. I have seen videos of cell phones causing flight instruments to act erratically and they can cause major issues if the airplane isn't specifically certified for it.
I have never had much luck with cellular data in flight.
This might just be a function of the kinds of locations where I fly, but in my experience the connection is never good enough to get reliable weather information. Once in a while you might get an update, but I wouldn't count on it.
A much better option (if you can afford it) is FIS-B, which has always worked reliably for me, especially when there really is weather out there (which is when you really need it to work).
In the US up until recently the answer was an emphatic (FCC-mandated) NO, but the FCC is considering relaxing those rules, and if those rule changes go through you will be legally able to use your iPad's cellular data connection in flight (provided the pilot in command deems it's not a hazard to the flight - so remember to tell yourself it's OK to use the iPad).
Pretty much every CFI I've flown with has ignored this rule, and I'll admit to occasionally checking weather on my phone in flight too. It sometimes works, but in my experience only at relatively low altitudes (I typically lose my cellular signal somewhere between 2500 and 3500 feet AGL. There are long, boring technical reasons for this but basically the way the cell site antennas are designed the signal covers the ground below where cell site is - there's not much signal aimed at the sky above it).
Since it only generally works on climb-out (when my pre-flight weather briefing is still "fresh") or as I'm descending toward my destination (when I'm typically doing other things like talking to controllers or trying to get the field's weather on the radio) I've not found it to be particularly useful to use cellular data to get in-flight weather / information updates.