How to Draw Melting Icicles
V, 15 bytes

Àévò^lYp2x&gt;òÀñd


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Fairly straightforward.

À               " Arg1 times:
 év             "   Insert a 'v'
   ò       ò    " Recursively:
    ^l          "   Break if there is only one character on this line
      Y         "   Yank this line
       p        "   Paste it below us
        2x      "   Delete two characters
          &gt;     "   Indent this line
            À   " Arg2 times:
             ñd "   Delete a line