No, not the webbed mushrooms in the caves, different concept here.
The Idea
To allow spiders that have been in an area for a while to start webbing trees. Webbed trees gain the ability to have web stretched between them, which if run into, will lower the player's sanity and slow them down temporarily (the stretched web would be destroyed after being run through). This (should) stack and refresh the duration with each web run through.
Actual webbing would be a new function for spiders from larger (i.e. non tier-1) spider dens OR even be a new thing that "orphaned" spiders do when they aren't sleeping.
Running through webbing will NOT give silk, only chopping down one of the trees it is connecting to will break it into a piece of usable silk.
The Purpose
To encourage maintenance of your world while also making it substantially more dangerous if left unchecked.
Concept Variations (not all meant to be used at once, just additional things for the idea)
Instead of slowing, running through webbing could make the player pause for a second or two to remove it from themselves (Webber would be immune naturally)
Webbed Trees could drop spiders when chopped down.
Webbed Trees could summon a spider when being chopped. (Spider spawn would be put on a cooldown to prevent fighting more than one per tree)
Webbed Trees could randomly spawn webs in between each other instead of requiring a spider
Web between trees can be of various thickness (stack count) for areas ignored too long. (tiered webbed trees)
"Orphaned" spiders would be more likely to start webbing trees (and maybe move into them afterward?)
Webbed trees could be a bit more flame resistant than normal and totally normal trees.
Spiked trees cannot be webbed.
Additional Thoughts
This might be used in PvP servers as a new form of trap. This could also be a new item for world gen.