Is "kinda" a word?

As you said, it means "kind of". It's very informal and you won't find it in dictionaries. In formal contexts, you can use "rather" with the same meaning, e.g.:

It was rather cold.

Note:

"kind of" is in the Merriam-Webster dictionary (see below). "Kinda"2 is listed as a "pronunciation spelling."

Definition:

1: to a moderate degree

2: in a way that approximates : more or less

Synonyms:

enough, kindly [chiefly Southern], fairly, like, moderately, more or less, pretty, quite, rather, relatively, something, somewhat, sort of

The Corpus of Contemporary American English (COCA) has 1650 incidences of kinda:

TOTAL SPOKEN FICTION MAGAZINE NEWSPAPER ACADEMIC
1650  172    1023    244      169       42

It is used overwhelmingly in fiction, and the few examples in newspapers and academic texts are almost exclusively in quotations of spoken English.

So, as the other answers have said, kinda is a pretty informal word, not used in formal texts except in quotations. I personally would only use the word in very informal situations. Its 1650 incidences in COCA are comparable to other adverbs, such as besides (1720), tight (1642), and regardless (1607). As to whether or not it is an “actual” word, I think this is pretty clear evidence that it is. As for its acceptability, it is listed in some dictionaries, including Random House and Merriam-Webster.

Wiktionary contains such words.

The entry for kinda (http://en.wiktionary.org/wiki/kinda) includes:

kinda

1. (colloquial) kind of

   I kinda hafta do this right now.

   That's kinda funny.

The NOAD reports that kinda is an informal contraction of kind of; it was first used in the early 20th century, and it was originally an American English alternation.

Kind of is an informal phrase for rather.