Quite surprised by all these big NOs.
I would say: it depends.
If competing and consequently having better chances at winning competitions are your goals, then your body type can definitely give you an edge.
As common sense goes, grappling-based disciplines is more suited to stocky, strong people. There are notable exceptions: Paulo Miyao is a 64Kg bjj practioner who regularly wins open weight tournaments at the highest level, but look for example at the height/weight ratio of, say, the first 10 competitors at any Judo Summer Olympics and you'll start to see a pattern.
In striking, on the other hand, agility, and, more importantly, reach are strong indicators of an athlete's potential. Again, Mike Tyson was shorter than most if not all his opponents, but he was an exception. Looking at MMA, in which striking has become more and more important in the latest years, reach advantage is statistically a big factor, as described here: http://fightnomics.com/category/blog/ufc-arms-race-incredible-shrinking-middleweight/
From my personal experience, I insisted in practicing judo for years, despite my long and slim body type, and even if not competing, during practice I was hitting the mat a lot. Even with much less experienced, yet 30kgs heavier, guys. In BJJ I also spent most of the time on my back, overwhelmed by huge, jacked-up, guys. Learning was significantly slowed down by this. When I tried boxing for a while, tables were turned, I was enjoying it, and learn.
So, if potential competitive results or training enjoyment are a factor in your choice, then yes, your body type matters.
If you are going for Tai Chi, or other not competitive arts, everything goes.