How to filter gathering facts inside a playbook?

Yes, that's possible, but not in the default behavior of gathering facts. Having set gather_facts to true simply calls the setup module as very first task of the play. This way you do not have any way to parameterize the setup module call.

But you can disable the default behavior and call setup yourself with the filter parameter.

- hosts: all
  sudo: yes
  gather_facts: False
  tasks:
   - setup:
       filter: ansible_*

Since you're working on a role and might not want to have this setup call in your role, you could make use of pre_tasks.

- hosts: all
  sudo: yes
  gather_facts: False
  pre_tasks:
   - setup:
       filter: ansible_*
  roles:
   - your_role_here

The Ansible way at the top of the playbook (Additional way):

----
- hosts: web
  gather_facts: True
  gather_subset:
    - network
    - virtual

Debug vars with:

  - name: Print some debug information 
    vars: 
      msg: |
          Module Variables ("vars"):
          --------------------------------
          {{ vars | to_nice_json }} 

          Environment Variables ("environment"):
          --------------------------------
          {{ environment | to_nice_json }} 

          GROUP NAMES Variables ("group_names"):
          --------------------------------
          {{ group_names | to_nice_json }}

          GROUPS Variables ("groups"):
          --------------------------------
          {{ groups | to_nice_json }}

          HOST Variables ("hostvars"):
          --------------------------------
          {{ hostvars | to_nice_json }} 

    debug: 
      msg: "{{ msg.split('\n') }}"       
    tags: debug_info

After this question was asked and answered, Ansible 2.1 added the gather_subset option to the setup module so its now possible to use the !facter,!ohai,network syntax described in the documentation rather than a regex filter:

- hosts: all
  sudo: yes
  gather_facts: False
  pre_tasks:
   - setup:
       gather_subset: !facter,!ohai,network
  roles:
   - your_role_here