To simplify things, the answer to the "Is K actually the Deckard's son?" question is no. (At the very least, this differentiates the movie from the similar daddy issues dynamic of Ford's role in Star Wars: The Force Awakens.) As the film thunders to its conclusion, which includes a thrilling fight in a car slowly filling with water, we get one last twist. K learns from the leader of the burgeoning replicant freedom fighter movement that Deckard's child was a girl. More specifically, his daughter is Dr. Ana Stelline, the kind-hearted woman who designs memories for replicants. K actually meets her earlier in one of the movie's more enchanting scenes.
That same beguiling tone returns as the film ends and Deckard reunites with his daughter, who must be kept inside because of an auto-immune condition that may or may not be real. The sentimental encounter is offset by the stark image of K slowly dying as blood pours out underneath his jacket and snow falls around him. Here Villeneuve and cinematographer Roger Deakins, who gives each meticulously composed frame a languid grandeur, echo the rain that falls around Roy Batty towards the close of the original. (To me, it definitely looked like K was about to die, though obviously there will be diverting opinions.) That constant twinning of plot points, creating nostalgic reverberations and deja-vu-like familiarity in nearly every scene, will either be your favorite or least favorite part of the sequel. It really depends on if you love getting lost in a somber blockbuster reverie.
How does all this relate to the wooden horse? On a thematic level, it represents K's yearning for humanity, a soul, and freewill. He wants to be "born, not made." Also, like the film itself, the wooden toy horse evokes nostalgia. It turns out that the wooden horse memory is Ana's and that it was embedded in K's memory as a safeguard to hide her identity. The specific motivations behind that decision are a bit confusing and will likely become more clear after a re-watch or two. Perhaps, if this film truly follows in the footsteps of its predecessor, it's a detail that will be further teased out in director's cuts that arrive in the future. After all, it wouldn't be a Blade Runner movie if every piece of the puzzle fell into place on first viewing.