You are in wireframe view like this. You can only see the surface of the skin modifier.
To be able to see through the surface so that you can see the vertexes you also have to activate XRay
You can do the same in solid view (note that here I am in solid view and I have XRay selected too)
You might have to make the 3d viewport window wider to be able to see those view modes.
OK, I am making progress. Still a way to go (to get things the way I want them) but here is a view of the progress I have made in drawing the snowman.
I also would like to share this video which I think some newbies might find interesting as part of their learning experience. Create quick branches using Skin Modifier
Another silly problem. While I am making progress building the snowman in the tutorial, I have hit a snag that I should not be having. If you look at the image below, you will see the model when I view it on the right side, but when I click on the #1 keyboard shortcut, you will see the orientation of the model on the right side.
I tried selecting everything in the model and then rotating it but for some reason, I do not seem to be able to get everything oriented so that when I hit the #1, it will be facing forward.
Any suggestions? BTW, I would be willing to share the model if anyone would care to look at it and tell me what the h*** I am doing wrong.
It looks like the snowman’s right arm is rotated forwards.
If you hit numpad 7 you get the view from the top from there you should be able to rotate and reposition it.
(the lower window is top view (numpad 7)
It is worth noting that in 3d it is best to look from different views because 3d is …well 3 dimensions.
I do appreciate your feedback. Yes, I use 7 for the top view to try to adjust things. The biggest problem to me, at least right now, is to get the model (as a whole) oriented so that when I hit the 1 key i see the front view. I have not been able to get things set up for that (as I showed in my image).
As I said, I selected all objects and tried to rotate the entire model so it would be facing forward when i hit the 1. key.
BTW, I think with the right arm, what I really need to do is rotate the top part of the are in a more forward direction. I think that was a modeling (?) mistake. The arm is actually in the direction I want it, just the top part is messed up a little.
Go to top view, select everything and rotate it until it is facing forwards.
The result. In top view forwards is down to the bottom (see the annotation)
Ps your snowman is looking good already. 
From top view
I had tried going to 7 and then rotating everything once before, but it did not work. As it turns out, the axis for things was not correct so I wound up having to move a bunch of stuff individually and I think I finally resolved the issue. I should mention that I also modified the right arm a little so now I think I have things ready for move on to the next tutorial which will have some more interesting things. However, during this process to clean thing up, I think it once more taught me some things that will be valuable in the long run.
Here is a revised version of the snowman model.
Yes, I did rotate the view just slightly so you could see that I made progress.
