Well assuming these are always the culprits, Windows' search will index the HDD when idle for so long. Normally this is a good thing as when you are not really using the PC for anything taxing it builds a rapid table of file locations for when you want to search the drive(s).
If this is interfering with your using the PC (like it is taking its sweet time ceasing and giving you back your CPU cycles--my complaint) you can turn off indexing
(which I do) and/or remove/turn off search (and instead use a better behaved 3rd party search engine like Copernic
, which I do).
As for the host.exe, this is pretty generic for a lot of things. I would guess it is probably also involved in the indexing, but it is possible that it is malware which I really hate to bring up. If the AV is up to date and your Internet habits are good this should not be the problem...or your HDD contents could slowing be being made available to some guy in Russia.