We have a lot of outbound links on our website to various high DA websites.
Would it help or damage our SEO if I make all of the links
First, there's no reason to
nofollow outbound links unless they're from unmoderated user-generated content (i.e. people could link to things you'd rather they didn't) or they've been paid for.
Second, only this week a fairly thorough study established that not only is linking out not damaging to your SEO, it's beneficial.
All outbound links rel=nofollow? This is common question that arouses in mind of those who avail SEO marketing services There can be only one reason to do so and that is you are linking to all spammy sites on which you do not trust. So this may give a hint to Google that you are doing spam. Which i think will not be good for your SEO. So use rel=nofollow only where it is necessary, and use rel=dofollow for trusted sites.
It does not affect whether you used nofollow attribute or not. But it is always good practice to moderate your outbound links. If you linked to good resources without nofollow attribute, then google crawl and pass PR to that URL, so that useful information rise up in search result.
If you used links without nofollow attribute, then Google pass-out some values to that link. There are many of webmaster disagree with me, But recently John muller said, we pass same/equaly PR to internally and externally links.
If you used links with nofollow attribute, then your PR will not be save, it will be sculpt. For example, you have webpage A, and there are only 5 outbound links, and 2 of them using nofollow attribute, then remaining 3 links gain only 1 PR, and your 2 PR will be sculpt. (Here we not used other factors link dumping factor for clear PR calculation).