Back to the OP, I could imagine there being a good old mix of nature/nurture ratios for various aspects of a dwarf's make-up. Hair colour (barring hair-dyes) could be 100% nature[1], whereas how could religious affiliation be there from birth? 100% nurture[2], methinks (at least in 'choice' of deity, though some mental nature would affect the 'uptake' of worship for the chosen being).
Stature would be part genetics, but a dwarf destined to be stout could be stunted by environmental factors[3], or a born-weakling toughened up by the local regime (if not broken by it, of course).
Some slight complication, obviously. As far as I can tell (haven't checked the wisdom of the wiki, nor spotted anyone reporting anything on here (but then I wasn't looking for it), the "great rolls of fat" trait is largely down to how much eating is done (although the degree of propensity may be elsewhere fixed), while I still assume that there's an inherited genetic component to the more general build.
Certainly when I practice Darwinian husbandry of my animals (slaughter the ones that have weaker characteristics, let the others breed, albeit possibly for an initial loss of meat fat resources in the butchery industry) I seem to end up with top-end creatures. But I haven't actually tried the opposite approach of slaughtering the biggest creatures and seeing if the offspring of the remainder tend to be smaller.
(Also, apart from the actual grazers, I don't know how some animals might accumulate their "great rolls of fat" or not... Maybe they all do anyway, as long as they aren't starved, just like growing more fleece.)
[1] Although there's a point where 'nurture', or at least different types of later-life experiences, could accelerate or decelerate the hair greying, or being lost.
[2] Although that might be 40% father, 40% mother and 20% other authority figures in the kid's life. Adjusted by various factors (absent parents losing their influence, strongly pious individuals counting more (assuming no clash where it puts the kid off, and decreases their own fervency, rather than increases it...)
[3] Or inherited epigenetic factors deriving from the parental/grandparental environment of the time, to mirror the real-world studies along these lines. In-game it'd just be considered a malleable heritable trait, perhaps with each generation having passed "imminent stature" into "actual stature" and "pre-imminent stature" into "imminent stature", and "pre-imminent stature" being entirely left to the winds of change in that generation.