Do you need the article 'the' in the following sentence. Please explain.
The gun felt cold to touch.
The gun felt cold to the touch.
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Idiomatically, including the in such constructions is far more common. From Google Books...
As @hjpotter92 comments, The gun felt cold is also fine. There's no real difference in meaning between any of these forms - just a slight shift in emphasis.
When the is included, we're more inclined to interpret touch as the sense of touch (anyone's, not necessarily that of the speaker or his subject). But without the, we're more included to understand it as the action of touching (probably performed by the speaker or his subject).
Obviously if we discard to [the] touch completely, the basic meaning remains the same (if the gun feels cold, this can only be established by touch). But if we consider...
His leg felt cold [to [the] touch].
...then without those last 2/3 words, it's possible to understand the sentence as meaning he sensed that his leg was cold (directly, through the nerves in his leg, not by touching it with his fingers, etc.). The other two possibilities (that he, or someone else, touched his leg and felt the cold) are both still possible.