  Refining a classical proof of Whitney, we show that any $4$-connected planar
triangulation can be decomposed into a Hamiltonian path and two trees.
  Therefore, every $4$-connected planar graph decomposes into three forests,
one having maximum degree at most $2$.
  We use this result to show that any Hamiltonian planar triangulation can be
decomposed into two trees and one spanning tree of maximum degree at most $3$.
  These decompositions improve the result of Gon\c{c}alves [Covering planar
graphs with forests, one having bounded maximum degree. J. Comb. Theory, Ser.
B, 100(6):729--739, 2010] that every planar graph can be decomposed into three
forests, one of maximum degree at most $4$.
  We also show that our results are best-possible.
