Enforcing HTTPS is becoming more and more common. We started using HTTPS where I worked previously (site had millions of hits per week) due to the fact that Firefox was assuming HTTPS if no protocol is defined, meaning users could type "websitename.com" and not find our website at all, as we only served over HTTP.
I'm sure there were SEO implications behind redirects, but I seem to recall that 301 was the suggested route. Definitely not 302.
Internet Explorer didn't give us any issues for 8, 9 or 10 - prior versions I couldn't say. Hopefully someone else here will know more regarding IE7. There is a link here which explains a few issues, though: http://msdn.microsoft.com/en-us/library/bb250503(v=vs.85).aspx
Honestly in this day an age, the number of people using browsers which do not handle HTTPS are likely to be few - it's such a standard now. My opinion is that we need to try and progress things rather than build things around that total minority who refuse to get with the times. Technology is about progress, after all.