My question involves a careless driving ticket from the State of: MT

Help!
I was driving home, adverse weather conditions, on a state hwy, speed limit posted 70mph. I was going 40-45 mph on icy roads with fog. I see a car in front of me, they put on their blinker to turn left. I touch the brakes-not much noticible slow down but I continue braking and slowing. I collide rear-ending the car in front of me. It crunches my license plate, some visible damage to chevy bumper of car in front of me. We both pull off the road, we get out of our cars-are you ok? we both say yeah we're ok, I give the other driver my contact info and call the wreck in, not on a 911 call, just regular. They send sheriff rigs, fire department. Cops checks with other driver who now states has neck, back pain. Cop calls in ambulance. They load driver into ambulance on back board with neck brace. Fire dept, 2 ambulances, 3 sheriff pick-up trucks...there were like 8 or 9 rigs there with lights flashing, sheriff takes down my info and says highway patrol is quite a ways off, lets me leave and go home
over an hour later, hwy patrol shows up where I work which also where I live(he was not on the scene), has the report wrong-he shows we were north but we were south bound. Says he has a long night in front of him, says he is doing me a favor not giving me reckless(5 points), and in front of one of my employees gives me a careless(2 points) with a fine of $135.00.
Is that right? I have a commercial driver's license, I have not had a violation, wreck or anything for, like +25 years...
code is V5134 02 with a fine of $135.00.
I just think this is extreme...how slow would have been slow enough? The roads had been deteriorating but nothing was sanded or gravelled or caution marked...
Honestly, I have never been involved in something like this and I have been driving in winter conditions in montana all my life.
How do I contest this? What liabilities do I face? worried...