There are various factors involved.
On roads, if they have been gritted, there won't be much ice (unless VERY cold). Even on 'side streets' tyres will have brought some salt/grit from main roads.
Car tyres get quite warm due to friction on tarmac - which is warmed too.
Off-road paths tend not to be gritted!
They won't get much grit dragged there by bike tyres - which won't be that warm either.
Old railway lines tend to be in cuttings which can be shaded - especially when tree-lined - or exposed on embankments which can be wind chilled.
Probably the biggest factor at present where air temperature is not much above freezing is latent heat. Basically this means that for ice to become water requires energy - not just a rise in temperature.
All reasons why it is important that the off-road network is gritted and monitored - long after the rest of the transport system has returned to 'normal'.