Having done this, I followed the Moving WordPress Codex Page to move my installation as safely as possible.
I did everything listed in that page, including moving files to the /htdocs/blog folder, checking the Permalinks in the settings panel, updating the old references to media files with the Velvet Blues Update URLs plugin, updating the Settings > Media ‘store uploads folder’, and checking menu links.
Now I’m using the /yyyy/mm/post-name permalink format, and my post links and pages work perfectly, while all the category or tag pages do not load and show a (webhost-themed) 404 error. You can try it yourself: the site is in Italian but I’m sure you’ll figure out what to click.
On the other hand, everything works fine if I disable permalinks and use just the plain siteurl.com/?cat=xx structure, but I don’t like it!
I strongly believe this issue is caused by something related to redirection, so I’ll list below the ‘sources of redirection’ for my website.