I doubt its a manifold leak if its a newish car. Toyota in my experience usually build things mechanically to a very high standard.
I believe the hunting of idle in cold temps is to do with the tune of the car.
Im unsure whether Toyota flash the same program into both manual and automatic cars, obviously despite what some people may believe, every car that comes down the assembly line is different in tolerances inside the motor and one generic tune flashed into every single vehicle does not make a car operate under optimum conditions.
Unfortunately Toyota have a history of making it near on impossible to be able to simply plug a laptop with an aftermarket tuning program into the OBD2 port which allows alterations to be made to the factory ECU.
If anyone here has played with an aftermarket program, you can tune out hunting at cold start, and the amount of parameters you can change and alter is mind boggling. So it boils down to what kind of conditions your car sees most often and tune it to suit, or if you are an avid enthusiast, you log and tune your car everyday of the week, year in, year out so you have a tune for every season from winter to summer.
If its a stock car in extreme cold, my advice would be to use an oil with good flowing characterisitcs at low temp to help turn the motor over easy and dont wait for the car to warm up, just get in and start driving to get it up to operating temp ASAP, dont rev the motor past 3 grand till the temperature gauge gets to normal.
Because of the cold, not only will the O2s take longer to warm up, there are other adjustments to consider such as IAC steps, coolant temp, fuel trims, commanded idle speed, AFRs, and alot more sensor info I wont delve into because it really is complex unless one has experience in tuning.