This root was primarily used as the basis for the word Q. coa “house”, which first appeared (without the root) in the Quendi and Eldar essay of 1959-60 (WJ/369). The root √KAW “shelter” appeared in various etymological notes from the mid-to-late 1960s (PE17/107-108, 164; VT47/35). The root √KAWA also appeared in the 2nd version of the Tengwesta Qenderinwa written around 1950, but there it was unglossed and had no glossed derivatives, so whether it meant “shelter” in the early 1950s is unclear.
The only published root with form similar to √KAWA prior to 1950 is ᴱ√KAẆA “stoop” from the Qenya Lexicon of the 1910s (QL/45), also appearing as kava- or cava- in the contemporaneous Gnomish Lexicon (GL/25, 27). The Ẇ is Tolkien’s usual representation of derivatives of ancient labialized velar spirants [ɣʷ] or [xʷ] (PE12/15-16). The derivatives of this root included words like ᴱQ. kauko/G. caug “humpback” and ᴱQ. kawa-/G. cam(m)a- “bow”, so it seems to have no connection to later √KAW other than its similarity in form.
Tolkien used this root and ones like it on-and-off for Elvish “thought” words throughout his life. The first manifestation of this root was in words from the Gnomish Lexicon of the 1910s like G. sana- “can, know how to, have knowledge, craft or skill” and G. santhi “knowledge, experience (in) or skill (in)” (GL/67), which suggests a (hypothetical) early root ✱ᴱ√SANA “know”, though such a root does not appear in the contemporaneous Qenya Lexicon. In etymological notes associated with the Ósanwe-kenta essay from 1959-60 Tolkien gave:
> √SAM mind, think, reflect, be aware. sāma a mind. sanwe an act of thinking, a thought (✱sam-we). ósanwe interchange of thought (between 2 samat). sanwekenda thought-inspection, thought-reading. sanwe-menta thought-sending, mental message (VT41/5).
However, in notes associated with óre that were contemporaneous with The Shibboleth of Feanor from 1968, Tolkien gave Q. sanar = “mind, reflector, thinker” (VT41/13), and in Late Notes on Verb Structure (LVS) from 1969 (LVS) Tolkien gave the root √SAN “think, use mind; ponder, consider (in thought)” with derivative Q. sanwë “(act or process of) thinking, thought” (PE22/158). Thus 1959-60 √SAM “think” >> 1968-69 √SAN “think”, perhaps a restoration of the Gnomish root from the 1910s.