Is there a way to print simple roots as Root objects?

expr = 3 - Sqrt[2];

Use ToNumberField to convert the expression to an AlgebraicNumber

expr2 = expr // ToNumberField

The short form display of the AlgebraicNumber is similar to that of Root

RootReduce will convert the expression back to the radical representation.

expr2 // RootReduce

(* 3 - Sqrt[2] *)

You can discover the polynomial with MinimalPolynomial:

p = MinimalPolynomial[3 - Sqrt[2]]
(*    7 - 6 #1 + #1^2 &    *)

p[x]
(*    7 - 6 x + x^2    *)

Root[p, 1]
(*    3 - Sqrt[2]    *)

From the documentation of Root:

For linear and quadratic polynomials f[x], Root[f,k] is automatically reduced to explicit rational or radical form.

You can wrap HoldForm only around Root.

Edit

p = MinimalPolynomial[ro = 3 - Sqrt[2]];

a = Select[Range[10], Root[p, #] == ro &][[1]] // Quiet;

hf = HoldForm[Root][p, a]

(*   Root(#1^2-6 #1+7&,1)   *)

hf // ReleaseHold

(*   3 - Sqrt[2]   *)