Verse 1:

In the prologue to this poem, Odin and Frigg visit mortals in human guise. They each foster a human child, Agnar and Geirrod. Clearly, they appear to and are indistinguishable from other humans, when they want to be. So naturally, they would wear clothing.

In Hávamál 49, Odin speaks of giving his clothes to "two tree-men in the field" [Váðir mínur gaf ek velli at tveim trémönnum], a statement that likely indicates that it was Odin who first clothed the newly created human beings, Ask and Embla, which he helped make from trees found along the shore of Midgard. The word used there are  váðir 'clothes(49/1); and  ript, 'cloth', 'linen'(49/5).`
 
In the sagas, Odin commonly appears as a one-eyed old man wearing a broad-brimmed hat and a cloak. In Grímnismál 1, Odin is depicted wearing a mantle or cloak, which catches fire.
 
The word for the garment here is feldr, meaning “a cloak, especially one lined with fur” (Cleasby-Vigfusson). The etymology of the word appears to be from falda, meaning “to wrap, to fold.” Related words are feldr-dálkr, cloak-pin; feldar-röggvar, “the patches or ‘ragged’ hairs on the outside of a cloak”; and feldar-slitr, “the tatters of a cloak”. Vigfusson remarks that feldr is never used of a woman’s cloak (called a möttull, or skikkja).
 
In Harbarðsljóð 6, Harbard accuses Thor of not wearing breeches, saying “barelegged you stand, wearing your beggar’s gear. You don’t even have breeches!” So can we surmise that Thor too wears a cloak or other loose-fitting garment that does not include pants?  
 
In agreement with this, Tacitus describes the traditional dress of the German people in Germania 17:
 
"A garment common to all is a cloak fastened by a brooch, or if lacking a thorn; they are otherwise uncovered, and spend whole days next to the hearth and the fire. The wealthiest are distinguished by clothing that does not hang loosely, like that of the Samaritans and Parthians, but fits tightly and reveals the individuals limbs. They also wear animal skins, those nearest the rivers without much concern, those further way more fastidiously, since they lack adornments obtained through trade.  They select the animals with care and, after stripping off the hides, fleck them with patches from the pelts of the beasts bred by the outer ocean and its unknown seas. In the manner of dress, women do not differ from men, except that they often drape themselves with linen mantles which they decorate with purple, and do not extend the upper part of their garment into long sleeves, but leave the fore and upper arms bare; the adjoining part of the breast is also exposed."