  A new precision measurement of the $W$ boson mass has been announced by the
CDF collaboration, which strongly deviates from the Standard Model prediction.
In this article, we study the implications of this measurement on the parameter
space of the $SU(2)_L$ triplet extension (with hypercharge $Y=1$) of the
Standard Model Higgs sector, focusing on a limit where the new triplet is
approximate $\mathbb{Z}_2$-odd while the SM is $\mathbb{Z}_2$-even. We study
the compatibility of the triplet spectrum preferred by the $W$ boson mass
measured by the CDF-II experiment with other electroweak precision observables
and Higgs precision data. We comprehensively consider the signals of new Higgs
states at the LHC and highlighted the promising search channels. In addition,
we also investigate the cosmological implications of the case in which the
lightest new Higgs particle is either late decaying or cosmologically stable.
