According to most style guides, yes, you need hyphens in compound adjectives.
(Note that this only applies to adjectives that come before the word they modify: in she was old fashioned, it is not necessary, because it comes after; in an old-fashioned woman, it is.)
The general rule is to use hyphens only where they are necessary to prevent ambiguity or where they save readers the embarrassment of having to reread a passage. In practice, not all compound adjectives are problematic without hyphens; however, in this case uniformity trumps other concerns. If compound adjectives are always hyphenated, you have something to rely on as a reader. This is an advantage in itself. Secondly, it is easier for writers if they don't have to think about whether or not the compound is still readable without a hyphen.
I have more or less paraphrased Fowler's perspective here, as in Fowler's Modern English Usage; but I believe most style guides reason along similar lines.