how to see cycle map but without the trees?

The "layers" that you can see on openstreetmap.org are images built from individual bitmaps aka "tiles", there is no simple way to remove features from these bitmaps after they have been generated.

The rules that turn OSM data (typically already processed in one way or another) in to bitmaps are called "styles". So what you want is a style without forests or a style with more visible contours. If you are not happy with one of the many many ready made maps generated from OSM data (see http://wiki.openstreetmap.org/wiki/List_of_OSM-based_services for some of them) then you will have to produce one yourself, see for example: https://switch2osm.org/ and other similar questions on this site.

For the pundits: yes, vector tiles could address the issue this to a certain point, however would still require a mechanism to change the style on the fly or for the user to provide a custom version.

Have you tried using Garmin Basecamp (free download). You will also have to download a map see:- OSM on Garmin. Some of these maps may show what you need, The level of detail can be also be varied through 7 levels in Basecamp. If you have a Garmin on your bike they often have map settings that also vari detail. My Garmin Nuvi 1310 car sat nav will also display an OSM .img file but I'd need an extra power supply for more than 2 hours use. It is also possible to build your own Garmin map with Mkg Map and to choose the map style there are type files and editors to style and re-stile them... i haven't tried the latter yet but i hope to soon as i want simple clear map that shows the footpaths clearly on mainly white map that contrasts well and will print without using too much ink.

Hi did you read these pages, http://wiki.openstreetmap.org/wiki/Cycle_routes with a lot of links to already made selections. Use the Garmin maps based on OSM or follow this link to http://www.openfietsmap.nl/ Im not shure if it is what your looking for, but other bicyclist use them frequently.