Yes you should start your cars engine and allow it to run for at least 1 minute in the spring and summer to get the engine oil circulating through the engine and then slowly drive off.
Driving off too soon can cause your bearings to starve for oil and lead to bearing failure.
In cold weather you need to allow your engine to get to operating temperature by idling it and then slowly driving off until the engine and coolant temperature gets to the correct operating temperature.
This allows the engine oil to warm up as well and thin out to allow the engine to get the oil too it better by allowing the oil to flow better.
Some people say that you don't need to warm your car up in winter before driving off but that is not true.
I used to believe that until one morning I started my truck which was a 90 Chevy Silverado and then within a few seconds backed out of the driveway and then accelerated down the highway before the engine warmed up enough.
The temperature outside was 10 F and the engine was running a bit rough and trying to stall but that wasn't the worst of it.
As I got a few miles out on the highway I heard a ticking noise and then a squealing and loud screeching noise and then my engine spun a rod bearing and the engine locked up after I got it off the road.
So the engine needed new rod bearings after that.
So now I allow a few minutes of the engine idling to warm up to operating temperature and get the engine oil circulating.
During warm weather you can usually drive off within a minute but during cold weather you need to idle the engine for a few minutes at least and then slowly drive off and around the block for a few miles or so until the engine warms up to operating temperature.
Then accelerate off slowly.
If you can take the slower roads to allow the engine to not have to work so hard and allow the oil to circulate.
Your engine also runs at higher idle and richer mixture when cold so your engine can stall and sputter until the engine is warmed up.