I have the free Adobe reader, but not the full app. Will the Adobe Sign task still work in Nintex?
All you should need is an Adobe Sign account - as long as you have that, recipients can sign via the browser, so no one signing anything requires any software (the signer doesn't actually need an Adobe Sign account either, just the sender)
Hope this helps,
I've played around with Adobe Sign. They have a free trial, I think it's 30 days. But with it you need a subscription. Works really well though!