Bring a spare battery for your smartphone. Heck, bring two in winter.
Cold temperatures can wreak havoc on any battery powering an electronic device. You'll surely use part of your smartphone battery for the usual daily tasks, but Moscow's low temperatures will claim the rest. Phones may display a charge as high as 40 or 50 percent before the sustained cold fools the phone into shutting down, thinking the battery is actually dead. Whether the battery holds a charge or not, you won't be able to turn your phone back on.
If this happens to you while you're exploring Moscow in the cold, you'll be happy to have a "jump-starter" with you.