I have a 2005 audi a 8 that starts up in the morning but after i drive it for a while then shut it off it spins over does not start til it sits for a while then it cranks back up

Check the gear box oil level sounds low to me i had a similar problem with a auto box car before and as for your steering it could be a worn steering rack if the oil level is good

Sounds like the ignition control box. It sets on one of the inner fenders and has 8 wires running to it.

check the connection on your battery terminal ends. if they are loose or corroded that could explain the intermittent no spark. also could be a short somewhere but id check the terminals first. I had that problem once and the car did all sorts of weird things. airbag light, check engine light, randomly wouldnt start until i would mess with the battery.

It sounds like it's getting more fuel then it is air check the fuel filter and the mass air flow sensor it regulates the amount of air send it to the computer and the computer breaks down how much gas to operate the vehicle and run smooth hope this helps text George

2005 engine shuts off while driving

could be battery cable to starter

check your battery it could be getting worn out and need replacing or it could be the starter itself too

oil change

perhaps you need a new cap and roter a new spark plug wire set. they don;t like moisture. also check to see if you have any broken or leaking vacuum hoses. the worse case senerio would be that your head gasket is leaking--at cold temps a little antifreeze will enter until everything warms up and it seals shut due to metal expanding. but since you say it's cold weather only--this probably wou;dn't be the case. good luck.