Neicey,

First, when you say "a Holy Spirit", are you meaning THE Holy Spirit, the third Person in the Trinity?

The answer to this would be "no". While the Holy Spirit is omnipresent (all present), He does not indwell all (only believers).

Some articles on the Holy Spirit:

The Holy Spirit by Edwin Palmer

How can a true work of the Holy Spirit be distinguished from that which is false? by John MacArthur

The Holy Spirit by A. W. Pink

The Holy Spirit's Work in Salvation by A. W. Pink

Grieve Not the Spirit by Robert Murray M'Cheyne

As to people believing the Holy Spirit indwells all, that would be the belief of universalists and those that deny Christ as the only Way, Truth, and Life.

True godliness is a sincere feeling which loves God as Father as much as it fears and reverences Him as Lord, embraces His righteousness, and dreads offending Him worse than death~ Calvin