I don't know that this is necessarily the case. It is not stated anywhere (other than bowhunting) that a person cannot carry a handgun, that is under the approved deer hunting calibers, while deer hunting. There are other legal season going on that a small handgun may be used for at that time. It obviously wouldn't be legal to use it on a deer, but to carry it isn't illegal I don't believe. If you can point me to where it says it is, please do so.
On the other hand, why carry the extra weight of a small handgun while deer hunting? If you need to protect yourself from someone or something while hunting I think the shotgun/muzzleloader in your hand will do just fine.
Coyote hunting is legal, but see how far you get carrying a rifle and a slug gun at the same time while deer hunting with the exception of the late doe rifle season? There are regs as to what is considered a legal weapon while deer hunting and which seasons and handguns are covered.
From the regulations.
Hunters may not carry a handgun while
hunting under an archery tag, unless they have an
unfilled transportation tag for a season that allows
handguns.
Shotguns: 10-, 12-, 16-, and 20-gauge shotguns
shooting single slugs only.
Muzzleloaders: Flintlock or percussion cap
muzzleloading rifles or muskets between .44 and
.775 caliber shooting single projectiles; muzzleloading
pistols .44 caliber or larger with a minimum
barrel length of 4 inches and no shoulder
stock or long barrel modifications. Muzzleloaders
equipped with electronic ignition are not allowed.
There are no restrictions on in-line or disktype
muzzleloaders. Riflescopes may also be used.
Handguns: Center-fire handguns .357 caliber
or larger, shooting straight wall ammunition with
an expanding-type bullet. Minimum barrel length
for all handguns is 4 inches. No shoulder stock or
long barrel modifications are allowed.
Only the following center-fire cartridges may
be used: .357 Magnum, .357 Maximum, .375
Winchester, .38 Super, .40 S&W, .401 Powermag,
10 mm Auto, .41 Remington Magnum, .41 Action
Express, .44 S&W Special, .44 Remington Magnum,
.44 Automag, .444 Marlin, .445 Super Mag,
.45 ACP, .45 Colt, .45 Super Mag, .45 Winchester
Magnum, .45 Silhouette, .451 Detonics, .454
Casull, .45-70 Govt., .460 Rowland, .460 S&W
Mag, .475 Widley Magnum, .475 Linebaugh, .480
Ruger, .50 Action Express, .50 Linebaugh, .50
Beowulf and .500 S&W Mag.
Hunters age 16 and under ma