The explanation is actually really simple - Internet Explorer can't use images in normal html drop down selection lists so it can't use tex either. In fact IE refuses to show even mathJax.
There are some workarounds like using javascript (jquery) that create lists that look like typical html drop down lists with image support - for example http://www.marghoobsuleman.com/jquery-image-dropdown - but such scripts have never been implemented to moodle or those question types and they don't work if javascript is disabled.
http://tracker.moodle.org/browse/MDL-19440
which is not related to the IE problem
The same issue, yes, but it is also an IE problem
http://moodle.org/mod/forum/discuss.php?d=123806#p543153
You can use asciimathml and MathJax in dropdownlists and firefox renders maths well in normal drop down selection lists but tex filter is using images and IE has no way to render tex filter images in selection list (drop down list).
Only Firefox can show maths in elements like
<select>
<option>maths a</option>
<option>maths b</option>
<option>maths c</option>
<option>maths d</option>
</select>
so if you want to use maths in drop down lists you can change those lists to some other elements like div or span and use css with some nice classes and styles to make it look like a drop down list. If select lists can be changed with jQuery to other html elements in those image drop down list scripts it is as well possible to use those other elements right from the start instead of select drop down lists.
And since it requires a major rewrite of code of that question type I fully agree when you said: "No likely solution as it is an HTML limitation." - in the near future