A slow cranking speed almost always is the fault of one of the following :
Your battery is no good ;even a new one can be defective or damaged. Sometimes people buy one that is too small for the car too in terms of cranking power even though it is the same size physically.
This usually shows up first and foremost on an unusually cold day.
Most auto store chains now offer free battery testing.
Your alternator is not charging the battery properly. Again testing at most parts stores is free.
Loose or corroded or broken battery cables.Usually easily found and fixed at the battery terminals rarely anywhere else unless the cables were damaged or removed and replaced while making other repairs.
Here’s the uhoh problem.
Your starter is on it’s last legs and will fail soon. If your car is getting old and the battery is a good new one and fully charged and the cables are tight and clean this is most likely the problem.
This is easily detected by checking the amount of current in amperes flowing out of the battery when you are cranking the car.If the ampere draw is out of spec either way the starter is usually going bad. This is sometimes a free test, sometimes not.
Don’t install an expensive new starter until it has been performed.It’s not a failsafe test but it comes close.
This is the sort of problem that should be fixed right away before it results in you getting stranded and paying for a tow to a shop not necessarily your first choice as well as paying for the repair.
And if it is well below zero F don’t expect your car to crank over easily in any case but the right oil changed at the proper interval can make all the difference sometimes.
Be sure it is the weight and grade spec’ed by the manufacturer for your local conditions.