There is a private function that turns DecisionTree into Tree: data=Table[x->Sin[x]+RandomVariate[NormalDistribution[0, .2]], {x, RandomReal[{-10, 10}, 400]}]; p=Predict[data,Method->"DecisionTree"]; MachineLearning`file23DecisionTree`PackagePrivate`toTree@p[[1]]["Model"]["Tree"]

Here is the one that does the reverse:

fromTree[tree_Tree, nominalDimension_Integer : Automatic] := 
 Module[{leafPositions, nominalPositions, numericalPositions, 
   nodePositions, numericalFeatureIndices, nominalFeatureIndices, 
   nominalSplits, numericalThresholds, numericalOrdering, 
   nominallOrdering, ordering}, 
  leafPositions = TreePosition[tree, _, {-1}];
  nominalPositions = TreePosition[tree, _Equal, {0, -2}];
  numericalPositions = TreePosition[tree, _GreaterEqual, {0, -2}];
  nodePositions = Join[nominalPositions, numericalPositions];
  nominalFeatureIndices = 
   TreeExtract[tree, nominalPositions, 
    TreeData/*Replace[Indexed[_, i_] == _ :> i]];
  numericalFeatureIndices = 
   TreeExtract[tree, numericalPositions, 
    TreeData/*Replace[_ >= Indexed[_, i_] :> i]];
  nominalSplits = 
   TreeExtract[tree, nominalPositions, TreeData/*Last/*(2^# &)];
  numericalThresholds = 
   TreeExtract[tree, numericalPositions, TreeData/*First];
  nominallOrdering = 
   Ordering@
    Thread[{nominalFeatureIndices, nominalSplits, nominalPositions}];
  numericalOrdering = 
   Ordering@
    Thread[{numericalFeatureIndices, numericalThresholds,(*-Reverse/@*)
      numericalPositions}];
  ordering = 
   Join[nominallOrdering, 
    Length[nominallOrdering] + numericalOrdering];
  MachineLearning`DecisionTree[<|
    "FeatureIndices" -> 
     NumericArray[
      Replace[Join[nominalFeatureIndices[[nominallOrdering]], 
        numericalFeatureIndices[[numericalOrdering]]], {} -> {-1}], 
      "Integer16"], 
    "NumericalThresholds" -> numericalThresholds[[numericalOrdering]],
     "NominalSplits" -> nominalSplits[[nominallOrdering]], 
    "Children" -> 
     NumericArray[
      Replace[{} -> {{-1}}]@
       With[{positions = nodePositions[[ordering]]}, 
        First@FirstPosition[
              positions, #, -FirstPosition[leafPositions, #], 
              1] & /@ {Append[#, 1], Append[#, 2]} & /@ positions], 
      "Integer16"], 
    "LeafValues" -> 
     NumericArray[TreeExtract[tree, leafPositions, TreeData]], 
    "RootIndex" -> 
     First@FirstPosition[nodePositions[[ordering]], {}, {1}, 1], 
    "NominalDimension" -> 
     Replace[nominalDimension, 
      Automatic -> 
       Replace[Max[Max[nominalFeatureIndices], 
         Min[numericalFeatureIndices] - 1], Infinity -> 0]]|>]]

Nikolay -- thanks so much for your response. The private function you mentioned:

MachineLearning`file23DecisionTree` PackagePrivate` toTree@p[[1]]["Model"]["Tree"]

Did indeed produce a visual of a tree. Unfortunately, the information in there is far to sparse to be of much help. I find that python's scikit-learn and the graphviz package at least tell you what is going on at each of the splits in terms of the gini index, the number of variables etc.

I'm gonna give this feedback to the Mathematica team. I find that not providing information of how a tree is split individual way makes a very difficult to work with Mathematica for this particular method.