Will the $300/mo car payment prevent you from qualifying for the amount of mortgage you are seeking with the amount you intend to put down?
If the answer is "no", then it would not impact your mortgage because even if it does impact your score, when you take a term of 15-years or less, the credit score no longer impacts the type of interest rates you get when you are using conforming (Fannie Mae/Freddie Mac) financing - see https://www.efanniemae.com/sf/refmaterials/llpa/pdf/llpamatrix.pdf and notice that the adjustments are for loan terms greater than 15 years.
And financing something new usually does impact your score - because of the credit inquiry & having a new trade line report. New trade lines often hurt scores for a few months afterwards, then from that point forward the scores will increase at a higher rate than they did before because you will have one more positive payment reporting each month than you did before.
How do you know if your $300/mo car payment will prevent you from qualifying? You'd really need to speak with a mortgage professional to see, but in general for investment property financing you want to keep your total debt ratio to 43% or less - including your current housing expenses (you say you have 100% equity - own it free & clear? still have to include the property taxes/insurance though) and the proposed housing payment too. If you have a renter lined up (or already in the home), then that rental income can go towards qualifying if you use a Fannie Mae loan program (Freddie Mac requires a 2-year landlord history though, so if you are planning on using rental income to qualify and don't have that history, seek out lenders who can offer Fannie Mae loan programs)... in that situation 75% of the rental agreement amount goes towards offsetting it's housing expenses (any excess over the housing expense gets added to your qualifying income).