If you have a fuel pressure problem the engine may start fine but will have difficulty accelerating due to a lack of fuel. If you have difficulty starting, but runs down the road fine, it's not a fuel pressure problem.
When the outside temperature cools and the engine is cold, the computer turns on the injectors a bit longer to enrich the mixture like a choke on a carburator. I suspect that you may have one or more injectors that are dirty or not flowing a good spray pattern. That's what's causing your rough idle. You probably need to have you injectors cleaned. You can buy the cleaners in a pressurized can that screws into your fuel rail. Then you should add a can of a good quality injector cleaner into your gas tank every couple of oil changes to keep the injectors clean.
You might also want to look at the brand of gas you are buying. Cheaper brands often do not contain enough detergent additives to keep the injectors clean. Brand name gasoline like Exxon, Shell, Mobil, Chevron are some the brands that contain enough detergents that you will not encounter too many dirty injector problems.
One last thought...an injector can be dirty or malfunctioning where is drips a little. If the vehicle sits all night, it can dump a lot of raw fuel into that cylinder. When you start the engine it may run rough unitl it burns up all that excessive fuel, and then the drip may be too small to upset the engine while driving at highway speeds. You will probabl see a small drop in fuel mileage if it's a serious leak.
...Rich