Which character looks like a horseshoe
There is no horseshoe emoji or symbol in Unicode, so people borrow letters with the same shape. The favorite is Ʊ, the Latin capital letter upsilon (U+01B1), which looks like a horseshoe with its open end pointing up. Its small form ʊ is the IPA sign for the vowel sound in "foot" and "put".
℧ is the inverted ohm sign (U+2127), once used for the mho, an old unit of electrical conductance. It is an upside-down Ω, so between the two you get both directions: ℧ with the ends up and Ω with the ends down. See the omega symbol and ohm symbol pages for more.
What the lucky horseshoe means
Iron horseshoes have been good luck charms in Europe for centuries. Iron was believed to ward off evil spirits, and an English legend says Saint Dunstan, a blacksmith, nailed a horseshoe to the Devil's hoof and only removed it once the Devil promised never to enter a house with a horseshoe over the door.
Which way to hang it is a long-running debate. With the ends up, like Ʊ, the horseshoe holds the luck in like a cup. With the ends down, like Ω, it pours luck onto everyone who walks beneath it. Both traditions exist, so pick the one you like.
How to type Ʊ
In Microsoft Word, type 01B1 and press Alt + X to get Ʊ, or 2127 for ℧. In HTML, write Ʊ for Ʊ. Phone keyboards have no shortcut for it, so copy it from this page.
For more lucky charms like 🍀 and 🧿, see good luck symbols, or browse letter symbols for other unusual letters.