Can a spending freeze solve the problem of the Italian enormous government debt?
This question is somewhat political, and runs into the area of “opinion-based,” which this site has to avoid. I am only going to attempt to discuss part of it. There’s some long-running economic debates involved, so I will try to describe the debates. I obviously have my own opinions.

One side issue: it is unclear in what sense is an “enormous” debt a “problem”, other than the technical issue of the European treaties? But since those treaties exist, I will put that aside.

As background information, we normally think about the size of the government as a percentage of GDP. So if nominal GDP is growing in steady state, so would government spending. Therefore, a “freeze” in euro terms, although that might be interpreted as unchanged, would be thought of as shrinking government spending relative to trend. In commonly used terms, it would be viewed by many as a mild austerity policy.

This leads us to the debate about expansionary austerity. Alberto Alesina is the economist most associated with the revival of this policy. I am not familiar with the more recent literature, but this paper by the IMF was critical of idea of expansionary austerity - IMF paper link. I would summarise the conclusions that there was a mild depressing effect on growth (“contractionary” versus “expansionary”), but one may note that this is just reducing the growth rate of an already growing economy.

I am not going to claim to give the “correct” answer, but the debate is this: will the cut in spending reduce growth, so that the effect on the denominator of the debt/GDP ratio of reduced spending is cancelled out? Realistically, it probably depends on the state of the cycle. Cutting spending right after a crisis when confidence is low may have a more dampending effect than when the economy is starting to grow more rapidly. In Italy’s case, one would need to do a detailed forecasting exercise to see how large the margin of safety is. 

However, freezing spending would only reduce the deficit if the tax take rises along with nominal GDP. The suggested policy is to cut tax rates. That enters into another bitter debate in economics, the supply side effect of tax cuts.

(As an immdiate disclaimer, it is possible to redesign the tax system so that a lower tax rate will imply a higher tax take; for example, eliminate a popular deduction. It does not sound like that is the case here.)

The original supply side debate was very strong in the era of Ronald Reagan, the “Laffer Curve” (an idea of economist Art Laffer) was that very high tax rates were counter-productive. Cutting taxes would raise incomes through growth, and so revenues would increase. In 2018, I do not know of anyone who would argue that this would happen right now in the short term (one or two years, say). I believe the consensus is that the improved growth will appear on a longer horizon. In the United States, there is a debate about “dynamic scoring” that discusses this. There are plenty of resources for dynamic scoring on the internet, this is a recent presentation by the CBO - link to CBO presentation.

So one could expect that such a policy might result in a higher deficit in the short term (1-2 years), but will the tax cut lead stimulate enouh new activity on a longer horizon - that leads to a falling debt-to-GDP ratio? That question would either require analysis by experts on the Italian economy, or it would be largely opinion-based.