If Red Nose was dominant like polled

What if Rudolph's Red nose was a dominant trait like polled.
Rudolph was special. Santa knew that and he realized it and used him for his benefit.
It was good having him guide his sleigh. There was only one Rudolph, no spare backup, would a lighted team of reindeers be better? But since Rudolph's red nose is a dominant trait this can avoided. Rudolph could be used as a breeding buck and breed some fawn or does.
Next year 1/2 the crop of flying reindeers could be red nosed.
This is short term since the source of  Red nose was only Rudolph. Inbreeding would occur.
Santa's has sourced a  fawn from a Siberian red nose line to keep some diversity. He will be flushing her to Rudolph next year. Heterozygous x Heterozygous has a 1 in 4 chance of being homozygous or 100% Red nosed.
When he gets homozygous or 100% polled  every reinder born could be Red nosed. It would not take long to have Santa's sleigh guided by all Red nosed reindeers. With a breeding plan this can be sustainable.
With Polled the Genetic base has widened. There are different lines and options.
You only need to believe and you can make it happen.