I've flown several high altitude balloon payloads. Usually people choose simple processors such as Atmels and PIC (the various Arduinos are very popular). For data logging and telemetry, those are plenty powerful enough. They are also cheap and require little power.
The Raspberry Pi isn't ideal for the purpose, partly because of its relatively high power requirement (2W vs maybe 50mW), and because the main thing you want in a flight computer is for it to be reliable, and you gain that by simplicity. On an Arduino there's so little to go wrong - no SD card, no USB, etc.
All of that said, there's no reason for not using a Pi if you want to use one. You do get a far more powerful processor, with much more memory, and with easily available SD file storage.
I'm flying a Raspberry Pi payload quite soon. I made it for 2 reasons. One reason is that the USB provides access to cheap webcams, meaning I can send down live images with the usual telemetry. The other reason is .... "because"
. My pi was sitting there just begging to be used for something interesting!
Now onto your questions:
"temperature expected" - outside the pyload it will get down to -50 degrees or so. Inside however is another matter. With good insulation (EPS), the heat within from your batteries/regulators/Pi will keep it quite warm. I doubt it will go much below zero.
"effects of radiation" - never heard of any issues.
"effects of near vacuum on electronic components" - none (not for the time they're up there, anyway.
"Then using GPS interface to determine altitude, detach the tether to the ballon." - That's possible, but mostly people just rely on the (latex) balloon bursting, usually at an altitude of 30km or so. It is possible to detach from the balloon, typically using some nichrome wire to cut the cord. Remember this has to be *above* the parachute for obvious reasons!
"The raspberry pi would store and execute (using gpio) things like GPS input, collect temperature data, and take some photos of course (perhaps by controlling a digital camera)."
All OK. I have GPS and webcam on mine. I'm not bothering with other sensors this time. Most people use a Canon digital camera with the CHDK firmware which then runs an intervalometer script to automate the picture taking, in which case there's no need to interface a camera to the Pi. In my case I want live images this time, so I'm using a webcam. There's not enough bandwidth to download large images during the flight hence no need to use anything of decent quality.