A cold (or excessively hot) battery cannot accept or supply power as readily as one in the 'zone', so recharging can be slowed as a result. The discharge is not as efficient when it is cold, so you might notice a difference if you were trying to really push the car.
Terminology can be confusing, but in the i3 lexicon, preconditioning is for the cabin only...to get optimum range, you need to set a departure time and have the car plugged into an EVSE to warm the batteries. That has a 1Kw resistance heater, and will try to warm the batteries to between 10-20C...the logic will turn that on up to 3-hours prior to your set departure time. If you also choose to have the cabin conditioned (heat or cool), then that will start about 20-minutes prior and maybe extend a bit after your selected departure time. That is a separate 'tick box' on the departure menu. Preconditioning the cabin can take a draw of over 2Kw, then add the 1Kw for the batteries, and your load will easily exceed the level 1 EVSE supplied in the USA, so you'll leave with less than a full battery. With the EVSE sold for countries with 230-240vac that comes with the car, you'll still potentially go backwards a little, but might not, depending on the ambient temperature when you ask it to run.