Cold emailing angel investors can be a great way to start having meaningful conversations about fundraising. You do however need to be careful about offering securities in the United States. There are strict rules around solicitation of funding. The most important of which is making sure the people you are sending to are accredited investors.
Once you have your list of prospects, which you can find on Angel List and other investment sites, angel investors are no different than any other important person you'd like to reach via cold email. Assume they get a lot of cold emails, so you'll need to do something different to stand out
Strategy #1 - Find someone to introduce you to them
This may sound obvious but there are several ways to do this. You can simply reference someone you have in common on LinkedIn. It doesn't have to be a direct referral. Another method might be asking around on Twitter who some great local angel investors are and then using that tweet as your intro to the person.
Strategy #2 - Be concise and focus on building the relationship, not just pitching the deal
All too often I see long emails from founders about their business that needs funding. I hate to break it to you, nobody is reading it. They may glance at your deck but they're immediately looking for a reason to say no. Only give them the minimum amount of information they need. They'll reach back out if they're truly interested.
If you approach this initial cold email as the start to a long term relationship, you are much more likely to get investment from them at some point. Perhaps not with this particular company, but play the long game, it's worth it.
Don't follow up more than twice. If someone is really interested in investing, you'll know. They don't need to be reminded of it 4 or 5 times, that will just annoy them and make them even less likely to invest.