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This is not an answer. I can't give one as I have no access to Windows. However, it describes an experiment that I think might cast some light on how each of your options is affecting the rendering of a slider.

When I run into a problem with the space allocated to a control, I find it useful experiment with variations that have a frame drawn around the control. This gives me a better visual assessment of the problem. So to investigate your problem, I built a grid of framed sliders with option variations.

Grid[
  Map[
    Slider[0.5, Sequence @@ #] &,
    {{{}, 
      {Appearance -> "DownArrow"}}, 
     {{ImageSize -> {Automatic, 50}}, 
      {Appearance -> "DownArrow", ImageSize -> {Automatic, 50}}}},
    {2}]]

I am running V10.2 on OS X, and on my system the above code gives

I conclude that

1. Changing the appearance of the slider thumb has only a slight effect on the height of the thumb and, thus, on the height of the allocated space.
2. The ImageSize option has no effect on the height of the slider thumb

These conclusions only apply to OS X and maybe only specific version of OS X I am running. I suggest that you run my experiment or a similar one on your system and see if your results differ.