For any ring R R let Λ ( R ) \Lambda (R) denote the multiplicative group of power series of the form 1 + a 1 t + ⋯ 1 + {a_1}t + \cdots with coefficients in R R . The Artin-Hasse exponential mappings are homomorphisms W p , ∞ ( k ) → Λ ( W p , ∞ ( k ) ) W_{p, \infty } (k) \to \Lambda ({W_{p, \infty }}(k)) , which satisfy certain additional properties. Somewhat reformulated, the Artin-Hasse exponentials turn out to be special cases of a functorial ring homomorphism E : W p , ∞ ( − ) → W p , ∞ ( W p , ∞ ( − ) ) E: {W_{p, \infty }}( - ) \to {W_{p,\infty }}({W_{p,\infty }}( - )) , where W p , ∞ {W_{p,\infty }} is the functor of infinite-length Witt vectors associated to the prime p p . In this paper we present ramified versions of both W p , ∞ ( − ) {W_{p,\infty }}( - ) and E E , with W p , ∞ ( − ) {W_{p,\infty }}( - ) replaced by a functor W q , ∞ F ( − ) W_{q,\infty }^F( - ) , which is essentially the functor of q q -typical curves in a (twisted) Lubin-Tate formal group law over A A , where A A is a discrete valuation ring that admits a Frobenius-like endomorphism σ \sigma (we require σ ( a ) ≡ a q mod m \sigma (a) \equiv {a^q} \bmod \mathfrak {m} for all a ∈ A a \in A , where m \mathfrak {m} is the maximal idea of A A ). These ramified-Witt-vector functors W q , ∞ F ( − ) W_{q,\infty }^F( - ) do indeed have the property that, if k = A / m k = A/\mathfrak {m} is perfect, A A is complete, and l / k l/k is a finite extension of k k , then W q , ∞ F ( l ) W_{q,\infty }^F(l) is the ring of integers of the unique unramified extension L / K L/K covering l / k l/k .