【Cold】 , 【cool】 , 【chilly】 , 【frigid】 , 【freezing】 , 【frosty】 , 【gelid】 , 【icy】 , 【glacial】 ,  【arctic】 mean having a temperature below that which is normal or comfortable.

【Cold】 is the general term, often implying nothing more than a lack of warmth. It may also connote discomfort. (see also: Suffer from a 【cold】 vs Suffer from the 【cold】 )

【Cool】 suggests moderate and often refreshing coldness, but when hotness or warmth is desirable it, too, connotes something disagreeable. (see also: 【Cool】 vs Composed vs Collected vs Unruffled vs Imperturbable vs Unflappable vs Nonchalant)

【Chilly】 implies coldness that makes one shiver.

【Frigid】 , 【freezing】 , and  【frosty】 imply temperatures below 32° Fahrenheit.

【Frigid】 stresses the intensity of the 【cold】 and 【freezing】 its congealing effect (as on man, vegetation, and water) while 【frosty】 applies rather specifically to times or conditions in which fine ice crystals are deposited from atmospheric moisture onto a 【cold】 surface.

【Gelid】 is equivalent to 【freezing】 , but it somewhat more often stresses the resultant discomfort.

【Icy】 , when used to indicate a kind of coldness, implies frigidity so great as to be painful and cutting; it is applicable chiefly to winds, storms, and water.

Basically  【glacial】 is very close to 【icy】 , but its later association with glacier has given it an ambiguous cast in many locutions; thus, a 【glacial】 lake might be, according to context, either a painfully 【cold】 lake or one formed by the action of a glacier.

【Arctic】 is the strongest of these words in its suggestion of intense coldness. It connotes the frigidity of the polar regions and is usually a hyperbolic rather than an exact term.

When applied to persons, their temperaments, their acts and words, and their responses to stimuli, these words are also marked by differences in implications.

【Cold】 suggests absence of feeling or emotion, or less than normal human sympathy, friendliness, sensitiveness, or responsiveness.

【Cool】 (see also 【COOL】 2) stresses control over one's feelings or emotions, and therefore absence of excitement or agitation.

【Chilly】 , 【frosty】 , and 【freezing】 usually stress the effect of another's coldness: 【chilly】 connotes a depressing or repressive influence while 【frosty】 connotes a checking or restraining of advances and 【freezing】 connotes a blighting or repelling.

【Frigid】 suggests such a deficiency of natural feeling as is abnormal or repellent; it is specifically applicable to persons who are sexually passionless and averse to sexual intercourse, but it is often applied to things which are not, but by their nature should be, impassioned or infused with feeling or warmth.

【Gelid】 and 【icy】 suggest a discomfiting chill (as in manner or conduct), the former sometimes stressing the power to benumb, the latter the power to pierce or stab.

【Glacial】 suggests a chilling lack of vitality or animation.

【Arctic】 frequently adds to 【frigid】 a connotation of remoteness from all that is human or referable to humanity.