By the creamy, swirly look of it (as seen in pic above) + by the name of it => This cocktail must contain ice cream or at least cream-cream, no?

No.

(If I’ve now gotten it in your head that you simply must have an ice cream-based cocktail tonight, I’ve got you covered.)

But it is sweet, a-doy, and that’s thanks to the hit of grenadine.

Now, even though it’s called the Sweet Martini, and even though I just told you it’s sweet, let’s back up a moment and acknowledge that this isn’t the kind of sweet that passes for sweet nowadays. (I’m gonna stop saying “sweet” so much from here on out. Cool? Sweet.) What I mean is, this isn’t some sugargasm. This isn’t a Cosmo or a Type 2 Diabettini or a Sloe Comfortable Yo’ Mama Shops at Target (wuh? I may be tipsy).

This is sweet-as-the-opposite-of-dry, not sweet-as-a-molasses-sundae-with-sprinkles-on-top. It’s grownsed-up. It’s very 1960s. And it’s time you tried one. 

Now see, the pic below is much more witches’-brew than Candyland-princess. So, you know, focus on that.

The Sweet Martini

(As published in, ahem, The Big Book of Martinis for Moms)

1 ½ ounces dry gin

1 ½ ounces sweet vermouth

¼ ounce grenadine

Lemon twist, to garnish

Pour your gin, vermouth and grenadine into an ice-filled cocktail shake and shake vigorously for about 20 seconds. Strain into a chilled cocktail or martini glass and add your garnish.