mitong's explanation is right. にmakes an adj(本当です) into adverb（本当に）, but it's still understandable without に, and we do drop it sometimes in very casual conversation. 絶対にだめ(absolutely, 100% NO) and 本当にだめ(really, surely NO) are slightly different as you can see. So it's just matter of context. とても寒い(very cold) and本当に寒い(really cold), as well.

The word "hon-tou" = 本当(ほん-とう) may be considered as a noun or predicate, which has a meaning of real and right (as suggested by the other respondent). In terms of adjective usage, it is grouped as a na(な)-form adjective, and thus, when used as an adverb (meaning "really"), it is generally written as "hon-tou-ni" = 本当に(ほんとう に) . In my personal point of view, however, "hon-tou (ni)" is an adjective/adverb to describe something positive. Hence, for the term "da-me" = だめ, which is a negative term, I would say that they do not well match together. If you want to say "really No", then I would suggest to use "ze-t-tai" = 絶対(ぜったい) instead, i.e., 絶対(に) だめ! On the other hand, for the term "samu-i" = 寒い(さむい), you may use "tottemo" = とっても, meaning "very (much)" to emphasize the coldness. Hence, it can be said, 今は とっても 寒い, meaning "Now it is very, very cold". ciao ciao / じゃね。

ほんとう means [real/really, sometimes means very], right. It's better to say ほんとう[に」さむい / ほんとう[に]だめ。 = very cold / Is it really NO? You mean really NO?