It lurches forward in cold weather

Hello,

There could be a number of reasons why the engine has hesitation.
It could be due to a weak fuel pump, dirty fuel filter, vacuum leak, dirty mass air flow sensor, worn spark plugs etc.

The best course of action would be to take a look at induvial items and take appropriate action. Like cleaning out the mass air flow sensor, replacing fuel filter, checking for any vacuum leak and fixing if necessary.

Take a look at this helpful guide:

https://www.2carpros.com/articles/engine-hesitates

Go through this and report back to what you find.

Is the check engine light illuminated? If so scanning and retrieving the code(s) can help with the diagnostics.

https://www.2carpros.com/articles/checking-a-service-engine-soon-or-check-engine-light-on-or-flashing

If you have any questions, please feel free to let me know.
Thank you.