There's so much water in cucumbers that freezing them would make them go all soft and squidgy (as happens with soft fruits, such as raspberries). So I very much doubt that your cucumber had been frozen.
People tend to forget that, just like potatoes, strawberries, etc, there are lots of different varieties of cucumbers, with some being far nicer than others. You've probably just encountered one of the poorer varieties.
Alternatively your cucumber could just have been a bit old. They tend to loose their 'crispness' quite quickly after picking.