Answer is C
EXPLAINATION:-
In weaken questions one must try to attack the conclusion of the argument. Because there is a logical error in the conclusion and by revealing the error, you can show that the conclusion is weak. A weak conclusion makes the entire argument invalid (if the argument is deductive) or uncogent (if the argument is inductive). Also remember in Weaken question, we can use New Information.
Lets try to do this here
The argument tells us that Plastic sleds have these qualities:- faster, bad handling (hard to steer), weak brakes (harder to slow).
"Plastic sleds became popular; they go faster than wooden sleds but are harder to steer and slow" ===> mentioned in passage
Now if something skids fast, cannot be stopped and cannot be handled, it will crash more frequently and more injuries will occur.
The argument also tells us that Plastic Sleds have been used for 10 years but the rate of accident was higher only last year.
Ten years ago, smooth plastic sleds became popular ===> mentioned in passage
The number of children injured while sledding was much higher last winter than it was ten years ago. ===> mentioned in passage
Suddenly during last year the accident number has gone up? Why ? LET US INVESTIGATE.
A. A few children still use traditional wooden sleds.
This should actually cause less accident, since wooden sleds are safer. DISCARD OPTION A
B. Very few children wear any kind of protective gear, such as helmets, while sledding.
Well, children must not be wearing protection for 10 years. Why accidents have gone up last year only. doesn't answer this question. DISCARD OPTION B
C. Plastic sleds can be used in a much wider variety of snow conditions than wooden sleds can.
At first glance looks out of scope or irrelevant...BUT KEEP IT FOR LATER ANALYSIS
D. Most sledding injuries occur when a sled collides with a tree, a rock, or another sled.
So suddenly last year many trees, many rocks and many sleds appear? No indication about that DISCARD OPTION D
E. Because the traditional wooden sled can carry more than one rider, an accident involving a wooden sled can result in several children being injured.
This is reverse answer. More Wooden Sled = More injuries. So accidents should have been more 10 years ago when wooden sleds were used, not now. DISCARD OPTION E
What remains with us now is only option C which looked out of scope, or irrelevant
Now no matter, whether we like it or not it has to be the answer.
Lets Analyse it again
C. Plastic sleds can be used in a much wider variety of snow conditions than wooden sleds can.
Wooden sled can only be used in good weather when snow is soft and fresh, when there is no storm, when there is no fog, when visibility is good etc etc. Also given they are safer.
Plastic sled can be used in much wider condition such as when there is snow storm, still snowing, when the snow is hard and can cause injury on impact etc etc.
So may be last year something happened that has not happened in a long time after the introduction of plastic sleds. Finally after 10 years, last year snow conditions were bad. Now if people used wooden sleds , they could not sled because their wooden sleds don't have the capability. So NO sleds = NO accidents.
But Plastic sleds can still sleds in such extreme conditions. So people being stupid, ignored the bad condition and went out and coupled with the fact that plastic sleds are injury prone, People got injured and injured again and injured again. Stupid People 
AND WHY DOES THIS HAPPENED:- THE BLAME LIES ON PLASTIC SLEDS BECAUSE THEY CAN WORK IN A VARIETY OF WEATHER CONDITIONS (INCLUDING BAD CONDITIONS)
Thats what exactly option C says
CORRECT ANSWER C
In the past, most children who went sledding in the winter snow in Verland used wooden sleds with runners and steering bars. Ten years ago, smooth plastic sleds became popular; they go faster than wooden sleds but are harder to steer and slow. The concern that plastic sleds are more dangerous is clearly borne out by the fact that the number of children injured while sledding was much higher last winter than it was ten years ago.
Which of the following, if true in Verland, most seriously undermines the force of the evidence cited?
A. A few children still use traditional wooden sleds.
B. Very few children wear any kind of protective gear, such as helmets, while sledding.
C. Plastic sleds can be used in a much wider variety of snow conditions than wooden sleds can.
D. Most sledding injuries occur when a sled collides with a tree, a rock, or another sled.
E. Because the traditional wooden sled can carry more than one rider, an accident involving a wooden sled can result in several children being injured.