Did you mean operate or take off? You can't take off with anything more than light freezing rain because there are no holdover times listed. Meaning you can't do it. I am 121 though. (rules may be different)
I could be wrong, but I think that if a 135 company puts together a program and gets it approved, they can take off in icing conditions. But it does require putting together a program that is similar to 121 programs.
This is one of those things that if it isn't in the ops specs, you can't do it.
You must have a Ground Deicing Program. That can either be a Part 121-style program (OpsSpec A023) or a Pre-takeoff Contamination Check (IIRC OpsSpec A041). Pre-takeoff contamination check means visually checking the wing no more than 5 minutes prior to takeoff to determine the aircraft surfaces are clean. Most 135 ops use the latter.
Unless you are using a Part 121-style Ground Deicing Program, Holdover Tables are advisory (although it is prudent to follow). TECHNICALLY, there is no reason why a 135 operator can't legally takeoff in freezing rains IF nothing is sticking to the aircraft (very unlikely).
Part 121 guys and those using a full ground deicing program are bound by the Holdover Tables and because non exist for conditions like moderate/heavy freezing rain or heavy snow, they can not legally takeoff.
All is subject to the operator's procedures and AFM limitations.
DISCLAIMER: THIS IS AN INTERPRETATION OF THE REGS AND NOT A BEST PRACTICE
A specific restriction from operating in freezing rain was removed from our GOM a few revisions back. I was told the thought process was that since flight in freezing rain is prohibited by regulation (no flight in severe icing conditions) it was already covered and didn't need to be specifically addressed. Now we're debating freezing drizzle. Fortunately, the AFM for the aircraft I fly has a specific limitation against flying in freezing rain OR freezing drizzle. Done deal.