Deer have 48 chromosomes, where the DNA is. A fawn gets half its genetic makeup (24 chromosomes) from its sire and half (the other 24) from its dam. I like to think of it like 2 suits of cards, one clubs, the other hearts. If you lay the cards down in matching sets, kings together, queens together, jacks together, and so on down to the 2's, you'll get the visual I'm aiming for.
Now, lets say, each card tells the fetus deer what to do; the kings say how the antlers will one day grow, (clubs is spectacular, hearts is modest) the queens say what the color will be, (clubs is brown, hearts is white,) the jacks say how big it will get, (clubs, tall, hearts, short,) and the 2's say if it's a boy (clubs) or girl (hearts). Lets say, as you were laying the cards down, you were only careful to keep the sets together, but you didn't care which went down first, red or black, so as you look at the line of cards, some you see are red, some black.
All the information is there, its just that some is stronger (more visible in this illustration) than others. So if the card on top tells the developing deer that one day he will have huge antlers (of if a doe, one day she will carry that gene to pass on big antlers) then thats what the baby deer grows to show.
So, it appears that it's a different mix every time, but really, the future fawn only has a 50/50 chance for something that one or the other parent has. All species work this way, they just have different numbers of chromosomes.
This is the simple explanation, LOL! There are also various modifiers at work, and epigenetics, but that gets more confusing, =-D If you want a really cool website with movies with simple explanations, check this out,
http://learn.genetics.utah.edu/ I had fun watching the movies, =-D