Conveniently, this is part answered by CBO in Projected Costs of U.S. Nuclear Forces, 2021 to 2030:
If carried out, the plans for nuclear forces delineated in the Department of Defense’s (DoD’s) and the Department of Energy’s (DOE’s) fiscal year 2021 budget requests, submitted in February 2020, would cost a total of $634 billion over the 2021–2030 period, for an average of just over $60 billion a year, CBO estimates.
This compares to 700B$ year total budget for DoD.
It doesn't seem that nukes are a very high cost item, once you have initially built up the military industrial complex to support them. They also may not need as much training to operate at a sufficient efficiency level.
Unlike say a jet fighter where a pilot who doesn't fly frequently, typically at a cost of $15-35k an hour, is just not a very useful jet fighter.
And a lot of the US nuclear arsenal is pretty old, yet still perfectly functional. That's probably due to the limited scope for defensive measures: an ICBM/SLBM will get through. If an arms race redevelops, with regards to defensive systems, expect renewed spending on delivery systems that evade countermeasures.
Although that same CBO report did warn that US delivery systems are just getting too old in absolute terms, which is apparently what is driving some of those costs in the coming years:
The nation’s current nuclear forces are reaching the end of their service life, and some delivery systems may not be capable of having their service lives extended further. U.S. nuclear forces consist of submarines that launch ballistic missiles (SSBNs), land-based intercontinental ballistic missiles (ICBMs), long-range bomber aircraft, shorter-range tactical aircraft carrying bombs, and the nuclear warheads that those delivery systems carry. Over the next two decades, essentially all those systems will have to be refurbished or replaced with new systems if the United States is to continue fielding those capabilities.
I am also going to add the UK's Trident replacement program since that is an upcoming consideration for the UK. To put that in context, the UK defense budget is in the £45B range.
UK MoD puts replacement only at 41B£. However, it's more expensive if costed over the whole lifetime.
The Campaign for Nuclear Disarmament puts the overall cost over the 30 years at £205bn. Reuters, in an analysis last year that was disputed by the MoD, put the cost at £167bn.
Either way, £200B of nuclear over 30 years needs to be compared to £1350B in total defense spending over those 30 years.
Last, since the UK example is contrasting acquisition vs total lifetime costs, let's take a look at Canada's mooted F35s comparison of acquisition vs lifetime costs to see a conventional weapons case:
The government released the KPMG report on 12 December 2012, which projected a lifetime cost at C$45.8 billion over 42 years and showed that the estimated cost to both purchase and provide needed upgrades and infrastructure was included the government's $9 billion figure given previously, although it did not include operating costs.
