Just so we understand your question: are you saying:
a. that when you turn the key, NOTHING happens, as in no noise for a second or two?
b. the car DOES immediately crank but takes a second or two longer for ignition to happen?
If a, then I'm envisioning a 1970's Oldsmobile that when one turns the key, it is dead silent for a second or two before the starter receives an electrical jolt to get ignition to occur.
If the latter, IMO, as long as ignition occurs, I think all is well. Ice cold spark plugs as well as starters tend to like toasty warm garages and don't appreciate being left to shiver outside.
Live it up: There will be plenty of time to be old when you die.
* '09 Vibe: 1.8 liter *
* '10 Hyundai Elantra Touring *
* '07 Honda Fit Sport *
On Deck: '22 Tucson or Sportage/'22 Subaru Crosstrek/'22 Corolla Cross