In front of the fuel tanks, the T-34 usually had those little black track-like thinks attached to the mudguard. They look too small to be extra links, and they have a strange edge as well -as if they were ice-cleats, or some other sort of attachments that would help the tracks gain better grip. But this is only my conjecture. What are those things?

you are correct they are indeed grousers to increase grip
shown below on a model cause i couldnt find any real world photos quickly

Grousers and Ice Cleats are not the same things.

They are ice cleats. They bolt onto the face of the tracks to give a better grip on ice.

Modern version


Grousers go on the ends of the tracks to extend their width and give better surface contact on soft ground.

By US nomenclature the T-34 ice attachments would be called grousers. The bars supplied with tanks in WW II were called grousers, and in the case of the M4 series, were stored in the grouser compartment at the rear of the upper hull. In fact, nearly any sort of protruding feature on the track face was called a grouser, such as "chevron grouser" or "parallel grouser".

The devices shown in Gino's last picture may have been called grousers (no references handy to check) but if so it would be because of the bars across the track face. Typically the end connectors with extensions to increase width and floatation were called extended end connectors.

KL

Thank you guys, you all have been awesome and very helpful. If I'd known how to use these things I'd have attached to the white-washed T-34s I've built over the years. Oh well. Great to learn something new