Something isn't quite right (and it's not just because the dogs have no legs). Is the sled supposed to be moving forward towards the stationary dogs? There would be no friction force to the left unless there was movement to the right. If the dogs have now stopped, then the sled might have forwards momentum (remember Newton's first law of motion) which is reduced by friction. I say "might" because you haven't  - or your teacher hasn't - made this clear.

If the dogs have stopped pulling then there will be no horizontal force pair, only the vertical pair you mention.

My money is on Newton's Third Law still being valid, even in New Zealand: every force has an equal and opposite force.

The weight of the sled is balanced by an upward reactive force that is due to compressing the snow, earth and rock beneath the runners.

The molecular interaction betwen the runners and the snow (i.e friction) generates a pair of forces as long as there is relative motion.

One of these forces acts on the sled, and causes an acceleration that opposes the forward motion.

The other force acts on the Earth to accelerate its rotation. Fortunately, it is massive enough to not be affected too much. (In any case, this is just restoring the momentum that the dogs originally took away by starting the sled previously.) The change of momentum of the Earth is ignored for problems like this, but it is the paired force with the retardation.

Inertia is not properly a force. It is the kinetic energy (energy due to motion). In this case, the inertia the sled got when it was started, is removed by the deceleration, and goes into warming up the runners and the snow.

Actually, I envisaged the sled moving from west to east because of the diagram. The momentum imparted to the Earth is in the direction the sled accelerates and decelerates, not necessarily in line with its direction of rotation.

You could ask your teacher what happens when the sled is steered round a curve at constant speed. In that case, the direction of the force against the side of the runners keeps changing, which is interesting.

There will be no friction if there is no horizontal velocity as Jiml stated as the sled would be stationary hence only vertical forces can be applied.

But assuming there is horizontal velocity to the right then this will be the net force and then you will have air resistance pointing to the left as well as friction as you have it in the diagram.