Cover, overspread, envelop, wrap, shroud, veil are comparable when meaning to put or place or to be put or placed over or around.
Cover may imply the putting or placing by a conscious agent or unconscious agency of something on top or on or over a surface (as of a circumscribed area or body).
In these uses cover often carries an additional implication of hiding, enclosing, protecting, or sheltering; indeed, in some use the emphasis is upon one of these implications, the basic idea being obscured.
In still another sense cover implies an extending so far as to include, embrace, or comprise something.
Overspread usually implies a covering by something that diffuses itself or spreads over a surface; the word carries no clear implication of concealing, sheltering, or protecting, but it does suggest the activity of something that flows, expands, or scatters until the entire surface is covered.
Envelop suggests the presence or addition of something that surrounds and therefore covers or nearly covers a person or thing on all sides; it is often used of a gas or a liquid or of clothing.
Envelop lends itself to extension and often connotes something impalpable or immaterial as the enveloping element.
Wrap comes very close to envelop in meaning, but it suggests something that folds or winds about so as to enclose rather than surround; the difference, although sometimes slight, is usually important to idiomatic usage; thus, one wraps (better than envelops) oneself in blankets or one wraps up (not envelops) several bars of soap.
In extended use wrap usually suggests something that enfolds, enshrouds, or entangles.
Shroud and veil, in their extended senses, imply a covering that protects, conceals, or disguises, but shroud usually emphasizes the density and veil the comparative tenuity of the surrounding element.