I've been struggling to find sources on this question. I know Scotts have been using peat as a means to toast malt for scotch whiskey production for centuries, but with it being such a plentiful resource in the highlands and bogs I'm certain it had to be used by those living in rural areas growing grain or raising livestock.
When you toast malts or grains using peat, the smoke and brine from the sea air dramatically affects the flavor of the husk, germ, and flour that results from the milling process. We know this because of peated scotch. If peat was being used for heating and cooking in the Scottish home, how would that have affected the taste of their food? How would it have affected what, specifically, they cooked? And would it have had any nutritional health benefits?
You may be looking too far back to find useful sources for the effects of peat on cooking. The use of peat as a primary fuel for cooking and heating continued long past the middle ages.
Dr Samuel Johnson discusses it's use in Scotland in his 1774 "A Journey to the Western Islands of Scotland", and Dorothy Hartley, in her 1954 "Food in England", goes into considerable detail about how it was used, what type of fireplaces, ovens and cooking utensils were particular to it's use and what type of food and flavours resulted from these restrictions. Peat was still in widespread use when she was writing and she bases her work on first hand information. She addresses a wide ranging history of fuels, fireplaces, ovens and local foods so for the particular questions you are seeking sources on (other than nutritional health benefits) Hartley is a valuable source.
I give you her introduction to the section on Peat. "Peat permeates a district. The water runs peaty, the air is acrid with the peat reek. Peat means bedding for the cattle, curing for the fish, smoking for the bacon; It is surgical dressing, it dyes wool, stains skins, flavours the tea and the whiskey. It is also strongly preservative."