Interpretations of this line appear to vary.
According to Bernard Lott (New Swan Shakespeare, Advanced Series. Longman, 1968, 1990), the line may mean
that he [Horatio] has not yet woken up fully to the surroundings and has left part of him downstairs in the warmth. Horatio is not in sympathy with all the tension that the others feel.
According to G. R. Hibbard (The Oxford Shakespeare, 1987), the phrase means "All's that's left of him"; he adds:
Compare Lychorida's description of the new born Marina as "this piece | of your dead queen." (Pericles, 3.1.17-18 and 20). Horatio humorously implies that he is shrinking away in the bitter cold.
According to Harold Jenkins (The Arden Shakespeare, Second Series. Methuen/Routledge, 1982),
The hand he [Horatio] offers is real enough, but the dark which conceals the rest of him enables him to reserve full participation. The sceptic is already characterized by his tone of humorous deflation.
In spite of the differences in interpretation at the literal level, these three glosses have something in common: that Horatio's humorous comment distances himself from the tension suggested by the interactions between the others.