Is it useful to split a table into a frequently used and a archive table?
Personally, I would split that table. Definitely consider Rick James' point about ensuring everything is Indexed properly and is being queried efficiently first, but, at the end of the day, you're removing 90% of the data that you have to sift through to get what you want.  Archiving that data will make queries faster by reducing row counts and shrinking the Index(es) considerably. There will be more Indexes because you'll have to duplicate them on your Archive table, so disk space will suffer a little, but my expectation is that performance will improve... 

UNLESS: 
The only part of this that jumps to mind that would KILL what I'm suggesting is if the data being moved to the Archive is accessed more than you think.  In that case, you're now querying two tables, totaling to MORE than what you had before (including duplicated Indexes/Keys); not only is there not a benefit, you've now taken more time (with more overhead) than your original setup would have taken.  

In short: you need to be VERY sure about how often that Archived data is being accessed, and HOW it's being accessed, before you move it.