Why does the preterite of verbs such as "deal", "feel" and "dream" have a devoiced dental suffix?

I am trying to explain the morphology of some irregular weak verbs. I could explain "leave-left" as the result of assimilation with v being originally intervocalic f, but I can't see the reason for the verbs as mentioned in the title. The only thing I notice is that they all have their stems ending in a liquid or a nasal. Any suggestions for this?

It seems to be unclear overall, but related to the phonological structure of these words in Old English through modern English. Aside from the nasal/liquid consonant generalization you mentioned, it seems all of the affected verbs had heavy rather than light roots in Old English. In addition, since they were (either generally or always? I'm not quite sure) class I weak verbs, most have front vowels (there is at least one exception, burn~burnt).

I read a paper about it, The Dental Preterites in the History of English (Aditi Lahiri) that has the following to say:

...The new process of open syllable lengthening is evident in these data, applying in the past tense forms of verbs with light roots (see also Lahiri and Dresher 1999; Lahiri and Fikkert 1999; Fikkert et al. 2006), for example, OE fremede > ME frēmed.

The lengthy literature on the split in behavior in the dental preterite, illustrated above, contains several possible explanations. For example, it has been suggested that the use of [t] in the preterite is an extension of the OE 3p.sg (thus sendeþ > sent) (Morsbach 1896) or was borrowed from verbs like ME cepte (Moore and Marck- wardt 1951). What remains unexplained, however, is why the [t] was extended only to the class of heavy roots, even when the roots ended in a sonorant (cf. ME felte > felte) class. The loss of the final schwa in the original trisyllabic past tenses like fremede > frēmed is also unclear, as is the absence of intermediate forms like frēmede. Brunner (1960), taking a pessimistic attitude toward these explanations, simply says that the reasons for these changes are not quite clear. (517)

Lahiri's explanation is as follows:

Moore and Marckwardt (1951) observe that the /t/ was generalized based on words like cepte; the question, however, is why. The explanation offered here is that it had become necessary to unambiguously mark the difference between the two past tenses, whose distribution was no longer transparent. By the time of the loss of the schwa, the original light verb roots had either been restructured as having an underlyingly long vowel (e.g., hōp-) or an underlying geminate (dinn-), which later degeminated. The past suffix assimilated to the root with the loss of schwa and forms like hōpt surfaced from hōped, clashing with forms like cept. That is, the surface forms did not reflect the difference between hōp(e) ~ hōped > hōpt and cēp ~ cept. One way of distinguishing the suffixes was to keep the underlying forms apart (i.e., not just allomorphs)—one suffix as /d/ and the other as /t/, introducing a distinction between -ed and -t with root-final sonorants, as in felt versus healed.

Another important reason for /t/ to be the special plural morpheme was that the only source for preterite /t/ was assimilation to root-final voiceless consonants in heavy roots that could later be shortened, as in cept. Thus, /t/ was always associated with vowel shortening and could be easily interpreted as indicating the special status of the level I suffix. (521)

I don't know if I really follow the argument, since by the time forms like hōpt occured preterite /t/ was not always associated with vowel shortening.

Lahiri mentioned earlier on that

In past tense forms with heavy roots, the preterite /d/ assimilates in voicing to the preceding, root-final consonant. This is the only context in Old English in which the coronal past tense marker is voiceless. (510)