Welcome to the Q&A Forum

No it's not. if the new domain which i guess has no authority or ranking capabilities at all you won't benefit from this, i would also not bother you, but there is no need if you solely want to dot his for better ranking.

a 302 would suggest the page will be back anytime soon since its a "temporary redirect"
While a 301 suggest the page is moved. So personally i would use a 302 so that the page your landing on keeps the juice but the user will be redirected to a login screen for example.

I would suggest to noindex those pages if they are really hidden for search engines. (noindex,follow)

Interesting reads:

• Save your website with redirect on Moz.com
  and - SEO Advice discussing 302 redirect on mattcutts.com

If the pages return a 403 they are not passing through any link equity. Why can't you 301 all of the old links to the new location. That would be the way. the 403's can really hurt your site + rankings. Just removing all old content and doing nothing else is not the way to go. all old urls should return 301 to the correct ones!

Good luck, its a nasty job but has to be done for your own good Cheers.

You asked a very similar question earlier: http://moz.com/community/q/are-links-with-query-strings-worse-for-seo

Like iQSEO-UK said back then we haven't seen big impact on SEO with urls with query strings and specially utm tracking. I personally havent had any issues as well with duplicated content, or results double in the search engines or something. When you 301 it, if will have some loss in juice, and i suggest with a canonical this does as wel a little bit, but nothing significant for sure!

This is not 100% a fact, but i think you will lose "some" juice but certainly not significant!